Grade Ten Bellwork Test Review

Here is a link to the same questions but will be much easier to read. Have fun!

Right Angle Trigonometry Word Problems

For each problem, draw a sketch of the situation, write the equation to solve the problem and then give the answer.

1.     A 10 meter ladder is leaning against a building. The bottom of the ladder is 5 meters from the building. How many meters high is the top of the ladder? Round to the nearest tenth. 10 meters

2.    A dog pen is in the shape of a right triangle. The longer leg measures 15 feet. The hypotenuse is 7 feet shorter than three times the length of the shorter leg. How long is the shorter leg? 8 ft

3.    A guy wire reaches from the top of a 39.32 ft pole to a point on the ground 15 feet from the pole. Find the length of the wire and the angle it forms with the ground. 42.ft and 69.12 degrees

4.    A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff? Man-friend 489.8  Cliff-friend 470.8

5.    A road up a hill makes an angle of 5.1 with the horizontal. If the road from the bottom of the hill to the top of the hill is 2.5 miles long, how high is the hill? 0.22 miles

6.    A ladder leans against the side of a building. The base of the ladder is 5 meters from the building, and the top is 12 meters above the ground. What is the length of the ladder and what angle does it form with the ground? 67.4 degrees, 13 meters

7.    A ski resort is installing tows on its new ski runs. One hill has a vertical height of 500m and is inclined at 42 degrees. Determine the approximate length of the T-Bar cable if it goes to the top of the hill and returns?

1494.48 meters

8.    From a point 12 m from the base of a flagpole the angle of elevation to the top of the pole is 42 degrees. How tall is the flagpole? 10.8 meters

9.    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? 57.5 feet

10. 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? 21.8 degrees

11.  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? 64.94 feet

12. 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 35 degrees. The distance from the bird to the observer is 25 meters. How tall is the lamppost? 14.3 meters

13. Looking down from the roof of a house at an angle of 23º (angle of depression) a shiny object is seen. The roof of the house is 32 feet above the ground. How far is the shiny object from the house? 75.39 feet

14. A tree casts a 60 foot shadow. The angle of elevation is 30º. This is the angle at which you look up to the top of the tree from the ground. What is the height of the tree? 34.6 feet

15. A lamp post is 10 feet tall and casts a shadow. The distance from the top of the lamp post to the tip of the shadow is 20 feet. What is the angle of elevation at the tip of the shadow on the ground? 30 degrees

16. An observer on top of a 60-foot tall lighthouse sees a boat in distress at a 5º angle of depression. How far is the boat from the base of the lighthouse? 685.8 feet

17. A tree casts a shadow 70 feet long at an angle of elevation of 30º. How tall is the tree? 40.41 feet

18. You are looking up at a fourth story window, 40 feet up in a building. You are 100 feet away from the building, across the street. What is the angle of elevation from you to the window? 21.89 degrees

19. A little kid is flying a kite. The string of the kite makes an angle of 30 degrease with the ground. If the height of the kite is 12 ft, find the length of the string that the boy has used? 24 feet

20.You are at a live performance and you are in the balcony. You are looking down at the stage at an angle of 40 degrees, if you at floor level under the balcony you would be 20 ft away from the stage. How high up is the balcony?

16.8 feet

21.  I am standing a point A on one side of a river and wish to measure the distance across the river to the corner of a house (H) on the other side.  While facing the house, I turn 90 degrees, I walk exactly 50 feet.  I now measure the angle from where I was to the corner of the house to be 18.23 degrees.  How far it is across the river from point A to the corner of the house? 16.47

22. A guy-wire must be attached to a 80 foot pole.  The angle that the guy-wire must make with the ground has to be 75.5 degrees.  Find the length of the wire required to make this work? 82.6 feet

23.  A device for measuring the cloud height at night uses a vertical beam of light that makes a spot on the clouds.  The spot is viewed from a point 140 feet along the ground and the angle of elevation is 64.4 degrees.  What is the height of the cloud? 292.20 feet

24.  While standing on a cliff 161 feet above the ocean, I see a sailboat in the distance at an angle of depression of 21.2 degrees.  What is the horizontal distance to the sailboat? 415.1 feet

25.  A wire holding up a 40 foot telephone pole is 48 feet long.  The wire is attached to the pole 10.5 feet below the top.  What is the angle of elevation of the wire? 37.9 degrees

26.  From a window in building A, I observe the top of building B across the 50 foot wide street at an angle of elevation of 74.25 degrees.  I also observe the base of the building at an angle of depression of 52.18 degrees.  What is the height of the building (hint: you will need to do two calculations and add them) 241.7 feet