Solution of triangles Questions and Answers

Solve the triangle. a=7.019 in c=6.013 in B=78.47° What is the length of side b? in (Round to the nearest thousandth as needed.) What is the measure of angle A? (Round to the nearest hundredth as needed.) What is the measure of angle C? (Round to the nearest hundredth as needed.)

Using the Law of Sines to find all triangles if a = 47°, a = 22.3, b = 26.3. Round to two decimal places. As in the text, (a, a), (B, b) and (y, c) are angle-side opposite pairs. If no such triangle exists, enter DNE in each answer box. For the acute angle 3 we have: B= degrees Y = degrees C = For the obtuse angle B' we have: B' = degrees degrees c'

A spotlight on the ground is shining on a wall 16m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.6m/s, how fast is the length of her shadow on the building decreasing when she is 6m from the building?

Using the Law of Sines to find all triangles if γ = 74.7°, c = 2, a = 2.05. Round to two decimal places. As in the text, (a, a), (B, b) and (γ, c) are angle-side opposite pairs. If no such triangle exists, enter DNE in each answer box. For the acute angle we have: α = β = b = For the obtuse angle we have: α' = β' = b'=

Solve the triangle. a=7 c=14 B=97.1° What is the length of side b? Select the correct choice below and, if necessary, fill in the answer box within your choice. B. There is no solution.

The pool you are working at this summer wants to open up a refreshment stand that is equal distance to the pool, the restrooms, and the volleyball court. If the pool, the restaurant, and the volleyball court are all vertices of a triangle which point of concurrency would you build the refreshment stand? The circumcenter, the incenter, or the centroid. Explain your choice.

An artist is attempting to stretch a canvas that is 6 by 8 inches. In order to check that the canvas is actually rectangular, the artist will measure the diagonal to determine if the corners form true right angles. What length should the diagonal of the stretched canvas be?

Solve for the missing angle: the angles are given in degrees, despite the lack of a degree sign sin (47)/18=sin(B)/17 ∠B= . Enter your answer as a decimal value. . You must be accurate to at least 3 decimal places. . Note that for these problems, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

Which of the answer choices could NOT be the measure of an unknown side of a triangle with two known side lengths of 10 and 45? 38 55 50 45

Solve the triangle. a=7 c=12 B = 99.8° What is the length of side b? Select the correct choice below and, if necessary, fill in the answer box within your choice. What is the measure of angle C? Select the correct choice below and, if necessary, fill in the answer

Solve the triangle. a = 59.79 mi, b=40.04 mi, C= 52.1° Find the length of side c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A c= mi (Round to two decimal places as needed.) B. There is no solution.

Explain how the angle-angle-side congruence theorem is an extension of the angle-side-angle congruence theorem. Be sure to discuss the information you would need for each theorem.

Consider a triangle ABC like the one below. Suppose that C= 101°, a=57, and b=66. (The figure is not drawn to scale.) Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".

The equation P = 3s represents the perimeter P of an equilateral triangle with side length s. Is there a proportional relationship between the perimeter and the side length of an equilateral triangle? Explain.

One side of an equilateral triangle is 10 cm longer than the side of a smaller equilateral triangle. The sum of the perimeters of the triangles is 168 cm. How long is each side of the larger triangle?

Find the height of the triangle with an area of 231cm² and a base of 22 cm. Be sure to include the units.

Environmental Science A geologist wants to determine the distance, AB, across a sinkhole. Choosing a point E outside the sinkhole, she finds the distances AE and BE. She locates the midpoints C and D of AE and BE and then measures CD. What is the distance across the sinkhole? E D 46 ft 8

Calculate the length of the hypotenuse of a right triangle that has sides that measure 2' and 3' 5' 6.5' 3.6' 13'

A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this. A. All sides of the triangle have the same length. B. All angles of the triangle have the same measure. C. All rotations take one half of the triangle to the other half of the triangle.

You are building a new desk for your room and decide to make it triangular in shape. You want to be able to put chairs on all three sides of the triangle so you want the legs to be in the center of the triangle. This is going to be tricky because you need to find the point where the triangle will balance in the center. This point where the triangle will balance is called the centroid. It is the point where all three medians of the sides of the triangle intersect. Now that you have learned about two points of intersections within a triangle please answer the following two questions. Which of the points do you believe is the center of gravity based on the description above? The centroid or the incenter? How can you tell from the description? Please come up with your own real-life scenario that could be accurately represented by either the centroid or incenter. Please explain which term you are describing, incenter or centroid, and how your real-life scenario fits the definition of the term you chose. Next, respond to two peers remarking in complete sentences on their real-life scenario. If they stated their real-life scenario was the incenter, explain why it was not the centroid. If their real-life scenario was the centroid, explain why it was not the incenter. Forum Directions: Put your cursor in the reply box below to start a reply to the topic. Enter your text. When complete, click Post Reply. Reply to at least two of your classmates. All posts and replies should be proofread for spelling and grammar and should be written in complete sentences.

In triangle ABC, segment BF is an angle bisctor and the m<ABF = 40°. What is the m<ABC? 13 40 O 80 90

An isosceles triangle had one angle that measures 96°. Find the measures of the other two angles and classify the triangle as acute, right, or obtuse. Select one: O a. 380, 380, obtuse triangle O b. 40°,40%, obtuse triangle O C. 42°,420, obtuse triangle O d. 46°,46%, obtuse triangle O e. 440, 440, obtuse triangle

Tameka's back yard has three trees that form a small triangle. She is planning to plant a flower garden in this triangular area and must calculate the area in order to buy the correct amount of fertilizer and mulch. She measures the following distances for the three sides of the triangle: 10.5 ft, 8.75 ft, and 5.75 ft. Calculate the area of this garden. Round your answer to the nearest tenth. A = ft 2

A right triangle with vertices J(4, 0), K(0,0), and L(0,5) is rotated around the x-axis. To the nearest tenth of a unit, what is the volume of the resulting three-dimensional figure formed? Approximate as 3.14. 83.7 units³ 104.7 units³ 251.2 units³ 314.0 units³

Two ships leave a harbor at the same time. One ship travels on a bearing S11 °W at 13 miles per hour. The other ship travels on a bearing N75 °E at 12 miles per hour. How far apart will the ships be after 3 hours.

At a certain time of the day, a television relay tower casts a shadow on the ground 1500 cm long. A nearby pole 15 meters tall, casts a shadow 1250 cm long. How tall is the tower? Label units. (Illustrate the appropriate similar triangles used in your proportion.)

The line segment with endpoints P(1,2) and Q(3,6) is the hypotenuse of a right triangle. The third vertex, R, lies on the line with Cartesian equation -x+2y-1=0. a. Determine the coordinates of R. b. Using vectors, show that ΔPQR is a right triangle.

Select all true statements. A. The incenter of a triangle is the intersection of the angle bisectors. B. The incenter is the same distance from all the vertices of the triangle. C. The incenter is the same distance from all sides of the triangle. D. In order to construct the incenter, all 3 angle bisectors must be constructed. E. The incenter is the intersection of the perpendicular bisectors of each side.

The cities of Fayetteville, Raleigh and Durham form a triangle. They are building a new baseball stadium. How should they determine where to place the stadium so it is the same distance from all three cities to the stadium? Assume a direct path. OTreat the cities as sides of a triangle. The new baseball stadium should be built at the cities incenter. Treat the cities as vertices of a triangle. The new baseball stadium should be built at the cities incenter. Treat the cities as sides of a triangle. The new baseball stadium should be built at the cities circumcenter. Treat the cities as vertices of a triangle. The new baseball stadium should be built at the cities circumcenter.

Solve the triangle. a = 16, b= 12, c=5 (Round to one decimal place as needed.)

Three sidewalks cross near the middle of City Park, forming a triangular region. Levi donated money to the city to create a fountain in memory of his father. He wants the fountain to be located at a place that is equidistant from the three sidewalks. At which point of concurrency should it be located? A. orthocenter B. centroid C. circumcenter D. incenter

Solve the triangle. a = 9, b=9, c = 9 Solve for the value of each unknown. A = (Round to one decimal place as needed.)

A triangular lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420 feet on the third. Find the measure of the largest angle formed by these streets. Which of the following equations can be used to solve the problem? 250^2=300^2 +420^2 - (2)(300)(420)cosx 300^2 = 250^2 + 420^2 - (2)(250)(420)cosx 420^2 = 300^2 + 250^2 - (2)(300)(250)cosx

An iron tank is constructed in the form of an isosceles trapezoid. Each base angle measures 105°, the length of the base is 10 feet, and each of the nonparallel sides is 12 feet long. Determine the length of a diagonal brace to the nearest whole number. 10 ft 13 ft 18 ft 24 ft

Ella selects backsplash a rhombus. Each side of the a tile for her that is in the shape of rhombus measures 4 inches. The diagonal opposite the smaller angle is 2.9 inches. What is the measure of the larger angle in the rhombus? O approximately 118.4° O approximately 131.6° O approximately 137.5° O approximately 147.4°

If you wish to show that two triangles are similar, which statement(s) is correct? You may choose more than one correct answer. It is enough to show that one pair of corresponding angles is congruent. It is enough to show that two pairs of corresponding angles are congruent. It is enough to show that two pairs of corresponding sides are in the same ratio. It is enough to show that all three pairs of corresponding sides are in the same ratio. It is not enough to have information about only sides or only angles.

If a dilation is applied to a triangle, then the image must be O a larger or smaller triangle. O a congruent triangle. O a triangle that is rotated about a given point. O a triangle that is flipped over a line of symmetry.

By a Pythagorean triple, we call a triple of positive integers a, b, c such that a^2 +b^2 = c^2 and the integers a, b, c do not have a common prime factor. Using a formula for the stereographic projection find a Pythagorean triple a, b, c such that the product abc is divisible by 200.

A marathon swim follows a triangular course marked with three buoys, A, B, and C. The distance from buoy A to B is 400 meters, B to C is 500 meters, and C to A is 600 meters. What is the largest angle the swimmers must turn between the buoys? 97.181° 82.819° 55.771° 041.410°

Two American flags of different dimensions are properly folded into two similar isosceles right triangles. The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4: 5. If the length of the hypotenuse of the larger triangle is 2 feet, what is the length of the hypotenuse of the small triangle to the nearest tenth of a foot? 0.1 ft 0.6 ft 2.5 ft 1.6 ft

A surveyor standing next to a hut on one side of a river sights a boulder on the other side and determines the angle from the hut to the boulder is 70°. She then walks 100 meters parallel to the river until she arrives at a tree. The angle to the boulder from the tree is 32°. How far from the hut is the boulder? 56.4 meters 104.1 meters 54.2 meters 96.1 meters

A carousel is being designed for the Spring Festival. The horses will be mounted to a regular hexagon and the hexagon is then placed on a revolving circle so that each vertex of the hexagon lies on the circle as demonstrated below. 10 feet If the circle has a radius of 10 feet, how long is each side of the hexagon? 10 ft 5 ft 100 ft √10 ft

Tina ordered a replacement part for her desk. It was shipped in a box that measures 3 in. by 3 in. by 12 in. What is the greatest length in whole inches that the part could have been? Be sure to show your calculations to prove your answer is correct.

Given ΔABC with m∠B=82, m∠C=48, and a = 16 inches, what is the length of b? 15.522 inches 19.101 inches 20.683 inches 21.321 inches

Recall that "to solve a triangle" means to find values for all the angles and sides that weren't already given values. Using your knowledge of the sine and cosine laws, solve the following triangles. a. Triangle ABC in which A = 65°, B = 35°, and AB = 7 units. b. Triangle XYZ in which z = 8.0 cm, y = 7.0 cm, and z = 5.5 cm. c. Triangle DEF in which D=73°, d = 14 cm, and f = 10 cm. d. Triangle KMN in which k = 90 cm, n = 80 cm, and M = 50°.

Select all of the right triangles. Triangle ABC with AB = 30, BC = 40, and AC = 50 Triangle XYZ with XY = 1, YZ = 1, and XZ = 2 Triangle EFG with EF = 8, FG = 15, and EG = 17 Triangle LMN with LM = 7, MN = 24, and LN = 25 Triangle QRS with QR = 4, RS = 5, and QS = 6

Solve the following triangle. There may be two, one, or no such triangle. A = 142.54°, b= 5.995 feet, a = 8.858 feet Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Type an integer or decimal. Do not round until the final answer. Then round to the nearest hundredth as needed.) A. The triangle has one solution, B =° C=° c= feet B. The triangle has two solutions. The measurements for the solution with the longer side c are as follows. B₁ = ° C₁ = ° c₁ = feet The measurements for the solution with the shorter side c are as follows. B₂ = ° C₂ =° c₁= feet C. The triangle has no solution.

Which of the following is a true statement about the three angles of any right triangle? Each of the three angles has a measure of 60 degrees. Each of the three angles has a measure of 90 degrees. One angle measures 90 degrees and the other two angles have measures that are equal. One angle measures 90 degrees and the other two angles are acute angles. One angle measures 90 degrees, another angle is acute, and the third angle is obtuse.

Sketch the triangle and use the Law of Cosines to find the indicated value. Round your answer to the nearest hundredth. 19. Find the third side of a triangle with sides of 19 m and 16 m and an included angle of 43°.

A puzzle piece in the shape of a triangle has perimeter 28 centimeters. Two sides of the triangle are each three times as long as the shortest side. Find the length of the shortest side The length of the shortest side is cm. (Type a whole number.)