**Worksheet #11 – More Verbal Problems Involving Trigonometry**

Directions: On a separate sheet of paper, answer all of these questions. SHOW ALL WORK!

**Part 1: More Verbal Problems **

For 1-20, **answer the following questions in a sentence.**

- A fireman rests his ladder against a building, making a 57° angle with the ground. The bottom of the ladder is 28 feet from the base of the building. How long is the ladder?

- A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?

- A five-meter-long ladder leans against a wall, with the top of the ladder being four meters above the ground. What is the approximate angle that the ladder makes with the ground?

- A ramp has an angle of inclination of 20. It has a vertical height of 1.8 m. What is the length, L meters, of the ramp?

- A damaged tree is supported by a guy wire 10.0 m long. The wire makes an angle of 61 with the ground. Calculate the height at which the guy wire is attached to the tree.

- A helicopter is hovering above a road at an altitude of 24 m. At a certain time, the distance between the helicopter and a car on the road is 45.0 m. Calculate the angle of elevation of the helicopter from the car

- A tree that is 8.5 m tall casts a shadow 6m long. At what angle are the sun’s rays hitting the ground?

- John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. How tall is the tree?

- A tree casts a shadow on the ground. If the shadow is 95 feet long and the angle of the sun is 32º. How tall is the tree?

- A 16 foot ladder leans against a building. If the bottom of the ladder is 3 feet from the building, what angle does the ladder make with the ground?

- A pilot of an airplane in flight looks down at a point on the ground that is some distance away. The angle of depression is 28°, and the plane's altitude is 1200 meters. What is the distance from the pilot to the point on the ground?

- Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground?

- A building is 50 feet high. At a distance away from the building, an observer notices that the angle of elevation to the top of the building is 41º. How far is the observer from the base of the building?

- An airplane is flying at a height of 2 miles above the ground. The distance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?

- A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35º. The distance from the bird to the observer is 25 meters. How tall is the lamppost?

- If your distance from the foot of the tower is 20 m and the angle of elevation is 40, find the height of the tower.

- A ladder must reach the top of a building. The base of the ladder will be 25′ from the base of the building. The angle of elevation from the base of the ladder to the top of the building is 64°. Find the height of the building (h) and the length of the ladder ( m).

- From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º. Find to the nearest foot, the height of the tree.

- From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40º. How many feet, to the nearest foot, must the cat walk to reach the barn?

- A ladder 6 feet long leans against a wall and makes an angle of 71º with the ground. Find to the nearest tenth of a foot how high up the wall the ladder will reach.

**Part 2: Angle of Elevation (Find the missing ANGLE)**

- Find the angle of elevation of the sun when a tree that is 10 yards tall casts a shadow 14 yards long.
- A large totem pole in Alaska is 160 feet tall. On a particular day at noon, it casts a 222 ft shadow. What is the sun’s angle of elevation at that time?

**Part 3: Angle of Elevation (Find the missing SIDE)**

- From a point on level ground 25 feet from the base of a tower, the angle of elevation to the top of the tower is 78 degrees, as shown in the accompanying diagram. Find the height of the tower, to the nearest tenth of a foot.

- A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66 degrees. Determine the height of the tree to the nearest foot.

- To find the height of a pole, a surveyor moves 80 feet away from the base of the pole and measures the angle of elevation to the top of the pole to be 57 degrees. What is the height of the pole? Round to the nearest foot.

**Part 4: Angles of Depression (Find the missing ANGLE)**

- A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an entrance door 9.3 feet from the desk. Find the angle of depression from the spotlight to the entrance door.

**Part 5: Angles of Depression (Find the missing SIDE)**

- A person measures the angle of depression from the top of a wall to a point on the ground. The point is located on level ground 62 feet from the base of the wall and the angle of depression is 52 degrees. How high is the wall, to the nearest tenth of a foot?

- A lookout spots a fire from a 32 m high tower. The angle of depression from the tower to the fire is 13 degrees. To the nearest meter, how far is the fire from the base of the tower?

**Part 6: Angles of Elevation and Depression (Mixed)**

- An airplane that is 500 m in the air spots a boat at an 11 degree angle of depression. If the plane was to drop down a ladder to the water, how far would a man have to swim from the dropped ladder to the boat?

- If a tree 28 meters tall casts a shadow 32 meters long, what is the angle of elevation of the sun to the nearest degree?

- A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50 degrees. The distance between the ship on the surface and the sunken ship on the ocean floor is 200 meters. If the ocean floor is level in this area, how far above the ocean floor, to the nearest meter, is the ship on the surface?

- The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30 degrees. Which equation can be used to find the height of the tree?

b) tan 25 = ,30-?.

c) sin x = ,

25d) tan 30 = ,?-25.

**Part 7: Angles of Elevation and Depression (Challenge)**

- Suppose the angle of elevation from a swimmer to the top of a cliff is 45 degrees. The swimmer is x feet from the bottom of the cliff and the cliff is y feet high. Find two possible values for x and y.

- A lighthouse is built on the edge of a cliff near the ocean, as shown in the accompanying diagram. From a boat located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18 degrees and the angle of elevation to the top of the lighthouse is 28 degrees. What is the height of the lighthouse, x, to the nearest tenth of a foot?

**Part 8: Mixed Review**

**answer the following questions**

- Simplify:

- Simplify:

- Simplify:

- Find the missing side.

- Find the missing side.

- Find the missing angle.

- Find the missing angle.

Page 1