Solution of triangles Questions and Answers

For isosceles ΔPNQ, the vertices are P(-2a, 0), N(2a, 0). and Q(0, 2b). In terms of a and b, find the coordinates of the circumcenter of ΔPNQ. (The circumcenter is the point of concurrence for the perpendicular bisectors of the sides of a triangle.)

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. 3) B= 53.2° C=100.6° b= 31.5 A) A = 24.2°, a = 38.7, c = 17.4 B) A = 26.2°, a = 19.4, c = 40.7 C) A = 26.2°, a = 17.4, c = 38.7 D) A = 24.2°, a = 40.7, c = 19.4

A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 7 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 12 feet from the wall? a) 833/10 b) -833/20 c) -833/5 d) -833/10 e) 833/5

Starting from an airport, an airplane flies 210 miles west and then 110 miles south. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.) Provide your answer below: miles

Solve the triangle. a=8.895 in c= 6.110 in B=74.86° What is the length of side b? in (Round to the nearest thousandth as needed.) What is the measure of angle A? O (Round to the nearest hundredth as needed.) What is the measure of angle C? O

Solve the triangle. a=4.09 m c=5.83 m B= 29.8° What is the length of side b? (Simplify your answer. Type an integer or a decimal. Round to four decimal places if needed.) What is the measure of angle A? 1° (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.) What is the measure of angle C? ww****

Find the unknown angles in triangle ABC for the following triangle that exists. C=51° 30', b= 24.9 m, c = 35.3 m A. There is only one possible solution for the triangle. The measurements for the remaining angles are A = and B= B. There are two possible solutions for the triangle. The measurements for when B is larger are A= and B= The measurements for when B is smaller are A= and B= C. There are no possible solutions for this triangle.

A parallelogram has sides of length 14.4 cm and 12.4 cm. The longer diagonal has length 22.1 cm. Find the angle opposite the longer diagonal. What is the degree measure of the angle opposite the longer diagonal? (Round to the nearest tenth as needed.)

Solve the triangle a=4.16 m c=5.94 m B=25.4° what is the length of side B? (Simplify your answer. Type an integer or a decimal. Round to four decimal places if needed) What is the measure of angle A? (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.) What is the measure of angle C?

A flagpole 94.5 ft tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 35.4°, while the angle of elevation of the bottom of the flagpole is 26.9° Find the height of the building. The building is about ft tall. (Round to the nearest foot as needed.)

The equation for the area of a triangle is A = 1/2 bh Area = (1/2) (base) (height) The following information is provided to you: ΔABC≈ΔDEF The height of the ΔABC is equal to 9m and the base is equal to 4.8m. The height of the ΔDEF is equal to 15m. The area of the triangle DEF:

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 14 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Provide your answer below: x= ,y= ,z=

Solve the triangle ABC, if the triangle exists. B=35°18' a=38.6 b=30.8 A. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m A= m C= The length of side c = (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) (Round to the nearest tenth as needed.) The measurements for the solution with the shorter side c are as follows. mA= mC= The length of side c = (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) (Round to the nearest tenth as needed.)

Solve the triangle. A=68°, B=48°, a=11 C= b≈ C≈

Consider kite ABCD with diagonals intersecting at E, where BD is the perpendicular bisector of AC. Which is a pair of congruent triangles in the kite? Check all that apply. A ΔAABD ≈ ΔACBD B ΔAABC ≈ ΔAADC C ΔAABE ≈ ΔACBE D ΔAABE ≈ ΔAADE E ΔAADE ≈ ΔACDE

Use the law of sines to solve the triangle, if possible. B=36°, C= 27°, b=29 A= (Do not round until the final answer. Then round to the nearest degree as needed.) a= (Do not round until the final answer. Then round to the nearest tenth as needed.) c= 7.14 (Do not round until the final answer. Then round to the nearest tenth as needed.)

Starting from an airport, an airplane flies 110 miles west and then 210 miles northwest. How far, in miles, from the airport is the plane?

Given that a rectangle has a width of 3 feet and a perimeter of 34 feet, what is the length? Step 2 of 3: Without substitution, solve the formula for the unknown variable in terms of the known variables.

One leg of a right triangle is 49 inches longer than the other leg, and the hypotenuse is 91 inches. Find the lengths of the legs of the triangle. The lengths of the legs are inches. (Separate with commas - order does not matter.)

Which statement is true? When an altitude is drawn from the right angle of a right triangle it creates three similar triangles. When an altitude is drawn from an acute angle in a right triangle it creates two similar triangles. When an altitude is drawn from the right angle in a right triangle it creates two similar triangles. When an altitude is drawn from an acute angle in a right triangle it creates three similar triangles.

Which statement correctly describes two triangles that are similar? The distance between corresponding vertices are equal and the corresponding angle measures are the same. O The distance between corresponding vertices are equal, but the corresponding angle measures are not the same. The distance between corresponding vertices are proportional and the corresponding angle measures are the same. The distance between corresponding vertices are proportional, but the corresponding angle measures are not the same.

Transversal CD cuts parallel lines PQ and RS at points X and Y, respectively. Points P and R lie on one side of CD, while Q and Slie on the other side. If m/_PXY = 64.36°, what is m/_ZXYS? A 180⁰ B. 115.64⁰ C. 64.36° D. 25.64°

A ladder 24m long is placed on the ground in such a way that it touches the top of a vertical wall 15m high. Find the distance of the foot of the ladder from the bottom of the wall to the nearest tenth of a meter.

Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete. How can Han fix his proof? Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent. Side DB is congruent to side BD because they're the same segment. Angle A is congruent to angle because they're both right angles. By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB.

One side of triangle is 7 more than 2 times the shortest side. The third side is 23 feet more than the shortest side. The perimeter is 74. Find all three sides. The sides have lengths of___, and_____feet.

One of the angles of ΔABC has a measure of 63°. One of the angles of ΔDEF has a measure of 81°. If ΔABC and ΔDEF are similar, what is the measure of the smallest angle of ΔABC?

Assume a is opposite side a, ß is opposite side b, and y is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth. (If not possible, enter IMPOSSIBLE. Below, enter your answers so that ay is smaller than α2.) a = 9, b= 4, β = 24°

A person in a balloon which is 2,000 feet above the airport find the angle of depression to a ship out at sea is 21 degrees. Find the horizontal distance between the balloon and the ship. (Hint: Draw a picture) 5580.86 ft 5,210 ft 767.73 ft 2124.29 ft

Triangle ABC was dilated by 50%. What is the relationship between AC and A'C'? AC = (AC) (AC) = A'C A B' A% C C'

Triangle DEF has angles of three different measures. What are all the possible types of DEF? Select all that apply. Select all that apply: isosceles right scalene obtuse

On a dogleg golf hole, one golfer hits the ball 270 yards and then another 170 yards to reach the green. The angle between the two hits is equal to 100 degrees. How far would the golfer have to originally hit the ball for it to go directly to the same position on the green? 150.463 yards 106.746 yards 343.134 yards 117,740.903 yards

Which is the best definition of an equilateral triangle? A. A triangle in which no two sides are congruent B. A triangle that has at least two congruent sides A triangle that has three congruent sides

161 Draw a 45-45-90 triangle, label it, and properly state the lengths of each side for this special right triangle. You may use Desmos to draw your triangle. Insert your image here. . Draw a 30-60-90 triangle, label it, and properly state the lengths of each side for this special right triangle. You may use Desmos to draw your triangle. Insert your image here.

A child standing 4 feet away from his mother lets go of his balloon at the same height as his mother's line of sight! The balloon is rising at a rate of 1 foot per second. How fast is the angle of elevation from the mother to the balloon changing 3 seconds later?

What is the area of triangle ABC given m<B = 83°, a = 25 feet, and c = 40 feet? O 561.46 feet² O 496.27 feet² 186.23 feet² O 128.51 feet²

Kevin leans a 26-foot ladder against a wall so that it forms an angle of 71° with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary. Answer:

Triangle ABC is an isosceles triangle and side BC is congruent to side AC. If side AC equals 40 centimeters and AB is one half of side AC, what is the total perimeter of triangle ABC?

A triangle has sides with length 14 cm, 18 cm, and 22 cm. Is this an acute, obtuse, or right triangle? Right Acute Obtuse None

Two triangles are congruent if A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C.the angles in each triangle have a sum of 180° D. corresponding sides are proportional