Trigonometry Questions and Answers

LT 8 Three telephone wires connect two towers and the station How much wire is needed to connect Tower B to the station Tower A Station 130m 440 Tower B Round to the nearest tenth Just enter the number

A 6 foot tall man stands x feet away from an 18 foot tall street light as shown below Use similar triangles to express the length of the man s shadow in terms of x OX 3 0 2x 3x X N O x m

Find the value of x in the given right triangle 37 10 X x Enter your answer as a decimal rounded to the nearest tenth Enter

Nate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself On his first actual encounter with one of the trees Nate wants to know just how tall the tree is He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree 1 9 m 0 75 m 38 25 m Based on the information in the diagram how tall is the tree The diagram is not to scale The tree is

into and out of the valley They take the measurements shown Determine the height of the cliff to the nearest tenth of a kilometre 5 40 cliff 1 5 km 550 65

Katherine wants to determine the height x of a nearby tree She stands 53 feet from the base of the tree The measure of the angle of elevation from Katherine to the top of the tree is 41 Select all of the following that can be used to find the height of the tree Ox 53 sin 41 53 sin 49 Ox 53 cos 41 X 53 cos 49 Ox 53 tan 41 X X 53 tan 49

Find the exact value of the expression sec tan Select the correct choice and fill in any answer boxes in your choice below OA 88 Simplify your answer including any radicals Use integers or fractions for any numbers in the ex OB There is no solution sec tan 1

This image of a physics problem shows a block resting on a ramp PQP is the angle between the ramp and the horizontal and BW is oriented vertically Which quantity is equal to cos W OA O B OC O D sin P cos P 1 sin P W 1 cos P

A ship travels N36 E for 500 nautical miles In component form which vector represents this displace North 1 Picture not drawn to scale 500 NM O 500 tan 36 500 tan 54 O 500 cos 36 500 sin 36 O 500 cos 54 500 sin 54 O 500 sin 36 500 cos 36 O 500 sin 54 500 cos 54 East

Automatic Zoom 536544 viewContent 2714736 View A person who is 1 65m high stands 25 7m from the base of a building the top of a near building at an angle of elevation of 35 4 a Draw a diagram labelling all important information height of the building in meters to the nearest tenth

13 A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 9 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when ar s food safe from haars2 Explain why not

18 Lombard Street in San Francisco California is paved with red bricks and is a switchback road with a speed limit of 8 km h because of its extreme grade The angle of elevation of Lombard Street in one section reaches 15 Determine the grade of this section of road to the nearest percent STO Thinkstock 9 A hill on Oak Street has an angle of elevation of 11 A hill on Broadway Street has a 21 grade Which hill is steeper Hint Convert both into slone

Given that sin 0 necessary 3 and is in Quadrant III what is cos 0 Give your answer as an exact fraction with a radical if 3 Provide your answer below cos 0

The function graphed to the right is of the form y c cos x y c sinx y cos x d or y sin x d where d is the least possible positive value Determine the equation of the graph y N 1 1 2 X

Which equation matches the function shown in the graph 2 1 0 1 2 F4 O A OB O C OD NAT 2 nswer y 3 4 cos x 7 V E y cos x 1 cos x 1 y cos x kl 25 5T 3 2 E 4 HX 2 T

Find an equation for the graph shown AMADERA Mi 9 Type the equation of the given graph in the form y A sin wx or y Acos x y 0 Simplify your answer Type an exact answer in terms of Use integers or fractions for any numbers in the expression

Which of the following represents vector w 45i 28j in trigonometric form Round 0 to the nearest degree O w 53cos 32 i 53sin 32 j w 53cos 148 i 53sin 148 j w 35sin 32 i 35cos 32 j SH w 35sin 148 i 35cos 148 j

Question 3 1 point In building a tent Jada ties a rope from the top of a pole 3 meters high to a stake that is 4 meters away from the base of the pole Jada draws this diagram to help find the angle made between the rope and the ground Which equation can Jada use to find the value of x to O a Ob Oc rope Od 4 tan tan x x tan 314 tan x 3 4 4 3 pole 3

7D Explain why the values of the trigonometric ratios only depend on the angle a and not on the particular lengths x y z q r and s Your answer 7E If y z 0 7 what is the measure of angle a to the nearest degree

1 Kristina walks from her house around the park to the store She is interested in taking a shortcut through the park to save time Approximately how far away from her house is the store if she were to follow the path shown by the dotted line in the graphic below HOUSE 80 m O 134 m O 128 m O 180 m 200 m PARK 100 m STORE

From the observation deck of a skyscraper Meena measures a 45 angle of depression to a ship in the harbor below If the observation deck is 862 feet high what is the horizontal distance from the base of the skyscraper out to the ship Round your answer to the nearest tenth of a foot if necessary

Startl 36 12 3 36 2 45 7 22 45 x 14 22 8 15 16 15 30 60 X Special Right Triangles Directions Find each missing side Write all answers in simplest radical form Use your solutions to navigate through the maze Staple all work to this paper 14 11 30 2 24 15 sion 2 Simplest Radical Form 24 5 12 6 6 3 X 36 2 X 10 6 24 6 x 20 6 6 10 6 5 15 2 2 15 30 X 60 x 30 45 20 2 20 48 2 24 2 3 10 5 3 15 40 45 20 2 2 End 30 x 45 24 2 2 15 X X 4 30 45 28 3 7 3 7 2 2 15 4 15 2 30 X 24 x 60 7 6 45 Vas 14 3 42 4 5 8 5 x 30 16 3 X 60 48 Gina Wilson All Things Algebra 201

The expression O sin e O cos e O tan e O cot e 1 sin 0 simplifies to which of the following cos8

What are all of the solutions to the equation cos 30 cos 8 1 sin 30 sin O 0 O O 0 T 2 22 4 RIN An T 9 An

The expression Step 1 Step 2 sec x tan x 1 COS X tan x Step 4 1 Step 3 cos x sin x COS X 1 sin x secx 1 tan x 1 tan x 1 tan x COS X sin x COS X sin x Step 5 cscx COS X sin x Step 6 csc x cotx Which identity formula was simplified with the following steps

Which of the following expressions does cos x y cos x y simplify to O2 sin x sin y O 2 sin x cos y O 2 cos x cos y O 2 cos x sin y

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 29-foot ramp, to the nearest tenth of a degree, if its final height is 7 feet. The ramp's angle of elevation is (Round the answer to the nearest tenth of a degree.)

A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One rope is 121 feet long and makes an angle of 62° with the ground. The other rope is 115 feet long. What is the distance between the points on the ground at which the two ropes are anchored (just give one of the answers rounded to the nearest whole number)?

A 25-ft ladder is leaning against a building. If the base of the ladder is 7 ft. from the base of the building, what is the angle of elevation of the ladder? How high does the ladder reach on the building? Sketch the diagram, label the sides, and show the angle.

Use the following triangle to find the value of the indicated trigonometric function. Rationalize any denominators that you encounter in the answer.

Solve the triangle. Round to the nearest tenth. In ASTR, t = 23, r = 29, mZS = 111° mZT=36⁰, m≤R = 33º, s = 43 mZT=31°, m/R = 38°, s = 43 mZT=30°, m/R = 39°, s = 43 None of the other answers are correct OmZT = 27°, m≤R = 42°, s = 43

A statue in a harbor is approximately 325 feet tall. If the angle of elevation of a ship to the top of the statue is 23.7°, how far is the ship from the statue's base? The ship is from the statue's base.

Solve the triangle. Round to the nearest tenth. None of the other answers are correct mZK 113°, h 14, p = 13 mZK 113⁰, h = 15, p = 11 mZK 113°, h = 15, p = 10 mZK-113°, h = 15, p = 7

Solve the triangle. Round to the nearest tenth. m/C = 57°, a = 12, b = 22 None of the other answers are correct mZC= 57°, a = 15, b = 19 mZC = 57°, a = 12, b = 19 mZC = 57°, a = 9, b = 19

Use the inverse trigonometric keys on a calculator to find the measure of angle A.

A tower that is 100 feet tall casts a shadow 154 feet long. Find the angle of elevation of the sun to the nearest degree. The sun's angle of elevation is (Do not round until the final answer. Then round to the nearest whole number.)

A marine surveyor uses a rangefinder and a compass to locate a ship and an island in the vicinity of the coast on which she stands. The rangefinder indicates that the island is 386 m from her position and the ship is 589 m from her position. Using the compass, she finds that the ship ship's azimuth (the direction measured as an angle from north) is 319° and that of the island is 38°. What is the distance between the ship and the island?

If a wagon wheel had 15 more spokes, the angle between spokes would decrease by 54 degrees. How many spokes does the wheel have? A) 11 B) 5 C) 6 D) 2 E) 8

Choose all the right statements. Use Capital Letters ONLY. If you choose more than one letters, please arrange them in alphabetical order, please. A. cos 2A = cos² A- sin² A B. cos 2A = (cos A-sin A) (cos A + sin A) C. cos 2A = 2 cos² A-1 D. cos 2A = 1-2 sin² A E. cos 2A = cos² A+ sin² A

6. Draw a graph of at least two periods of the function gir) -3 cos (x/2t+ x/2)-2 by (a) plotting the points where the graph intersects the midline and (b) plotting the points where the graph achieves maximum and minimum values and (c) connecting these points with an appropriately curved sinusoidal wave List the period, midline, and amplitude of the function and label the scale on the axes

29. Determine the amplitude, period, midline, and an equation involving cosine for the graph shown in Figure 32. 30. Determine the amplitude, period, midline, and an equation involving sine for the graph shown in Figure 33.

To get a better look at the graph, you can click on it. The curve above is the graph of a sinusoidal function. It goes through the point (2, 0). Find a sinusoidal function that matches the given graph. If needed, you can enter π as pi in your answer.

Given right triangle ABC, right angle at C, side b = 6 inches, side c = 15 inches. Solve the triangle completely. Round all angles to the nearest degree and all sides to the nearest tenth of an inch. a= A= B=

Suppose tan(a)=5/6 where 0 ≤ α ≤ π/2. Find all solutions in [0, 2π): tan(2x)=5/6 x=

Without using a calculator, find all the solutions of tan(t) = -1 where -π < t ≤ π.

Suppose cos(a)=4/5, where 0 ≤ a ≤ π/2. Find all solutions in [0, 2π): cos(2x) = 4/5.

If construction costs are $156,000 per kilometer, find the cost of building the new road in the figure shown to the right.

Sketch the angle and write the sec and tan of the angle if the terminal side of the angle passes through (3, -6). Express each answer as a decimal rounded to the nearest hundredth. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end.

The following problem refers to triangle ABC. Solve it. Round your degrees and minutes to the nearest whole number. Round the sides to the 3 decimal places. b = 0.75, c = 0.507, A = 46°20'

Given oblique triangle ABC, side a = 12 ft., side b = 17 ft., side c = 10 ft., find the degree of the smallest angle (round to the nearest whole degree). DO NOT FIND ALL THREE ANGLES AND THEN CHOOSE THE MALLEST. Remember that the smallest angles is across from the smallest side. Be sure to type your answers to all parts in the answer box. Be sure to show all work on loose leaf as a file upload question at the end. This question is worth 8 points total. 1 for the answer and 7 for the work.