CTJan27 Online

1. 

   From a point on the ground, the top of a tree subtends an angle of elevation of 35°. If you stand 12 m from its base, how tall is the tree?

   $12 \cos(35^{\circ})$

   $12 / \tan(35^{\circ})$

   $12 \sin(35^{\circ})$

   $12 \tan(35^{\circ})$

2. A ladder leans against a wall making a 60° angle with the ground. If the foot of the ladder is 4 m from the wall, what is the ladder’s length?

   $4 \cos(60^{\circ})$

   $4 \sin(60^{\circ})$

   $4 / \sin(60^{\circ})$

   $4 / \cos(60^{\circ})$
3. 

   An observer 5 m from a building measures an elevation angle of 50° to its top. Find the building’s height above eye level.

   $5 \cos(50^{\circ})$

   $5 \sin(50^{\circ})$

   $5 / \tan(50^{\circ})$

   $5 \tan(50^{\circ})$

4. A ramp is set at 25° above horizontal and is 3 m long. How far (horizontally) does it extend from its base?

   $3 / \cos(25^{\circ})$

   $3 \cos(25^{\circ})$

   $3 \tan(25^{\circ})$

   $3 \sin(25^{\circ})$

5. Looking down 40° from the top of a cliff 20 m high, how far out to sea is a boat?

   $20 \tan(40^{\circ})$

   $20 / \tan(40^{\circ})$

   $20 \sin(40^{\circ})$

   $20 \cos(40^{\circ})$

6. A streetlight casts a shadow 8 m long when the sun’s elevation is 22°. What is the height of the lamp?

   $8 \cos(22^{\circ})$

   $8 \tan(22^{\circ})$

   $8 / \tan(22^{\circ})$

   $8 \sin(22^{\circ})$
7. 

   A 10 m beam is mounted such that it makes a 15° angle with the horizontal. How high above the ground is its far end?

   $10 \tan(15^{\circ})$

   $10 \cos(15^{\circ})$

   $10 / \sin(15^{\circ})$

   $10 \sin(15^{\circ})$

8. From 14 m away, the angle of elevation to a tower’s top is 58°. Find the tower’s height.

   $14 \cos(58^{\circ})$

   $14 \tan(58^{\circ})$

   $14 / \tan(58^{\circ})$

   $14 \sin(58^{\circ})$

9. A slide of unknown length makes a 30° angle with the ground and reaches a platform 2.5 m high. How long is the slide?

   $2.5 / \cos(30^{\circ})$

   $2.5 \sin(30^{\circ})$

   $2.5 \tan(30^{\circ})$

   $2.5 / \sin(30^{\circ})$

10. An airplane is spotted at a 12° angle above the horizon. If the plane is 200 m away horizontally, what is its altitude?

    $200 \sin(12^{\circ})$

    $200 \tan(12^{\circ})$

    $200 \cos(12^{\circ})$

    $200 / \tan(12^{\circ})$

11. A surveying rod of height 1.8 m produces a 2 m shadow. What is the sun’s elevation angle? (⇒ find angle)

    $\theta = \arctan(2 / 1.8)$

    $\theta = \arccos(1.8 / 2)$

    $\theta = \arctan(1.8 / 2)$

    $\theta = \arcsin(1.8 / 2)$

12. A guy‐wire is anchored 5 m from the base of a pole and makes a 70° angle with the ground. How tall is the pole?

    $5 \tan(70^{\circ})$

    $5 / \tan(70^{\circ})$

    $5 \sin(70^{\circ})$

    $5 \cos(70^{\circ})$

13. From a hilltop, you see a car at a 20° depression angle. If you are 50 m above road level, how far away is the car horizontally?

    $50 \sin(20^{\circ})$

    $50 / \tan(20^{\circ})$

    $50 \tan(20^{\circ})$

    $50 \cos(20^{\circ})$

14. A surveying instrument 1.5 m above the ground measures a 45° elevation to the top of a wall. How tall is the wall?

    $1.5 \tan(45^{\circ})$

    $1.5 + 1.5 / \tan(45^{\circ})$

    $1.5 + 1.5 \sin(45^{\circ})$

    $1.5 + 1.5 \tan(45^{\circ})$

15. A ladder leans making a 75° angle with the ground. If the ladder is 6 m long, how high up the wall does it reach?

    $6 / \sin(75^{\circ})$

    $6 \sin(75^{\circ})$

    $6 \tan(75^{\circ})$

    $6 \cos(75^{\circ})$

16. A kite is flying such that its string makes a 40° angle to the ground and the string is 25 m long. How high is the kite?

    $25 \sin(40^{\circ})$

    $25 / \sin(40^{\circ})$

    $25 \cos(40^{\circ})$

    $25 \tan(40^{\circ})$

17. From a point on level ground you see the top of a hill at 10° elevation. If the hill’s peak is 30 m above you, how far are you from its base?

    $30 \cos(10^{\circ})$

    $30 \sin(10^{\circ})$

    $30 / \tan(10^{\circ})$

    $30 \tan(10^{\circ})$

18. A 4 m ramp makes an angle of 18° with the floor. How high does it rise?

    $4 \sin(18^{\circ})$

    $4 / \sin(18^{\circ})$

    $4 \tan(18^{\circ})$

    $4 \cos(18^{\circ})$

19. An observer standing 9 m from a sign measures a 37° angle up to its top. How tall is the sign?

    $9 \sin(37^{\circ})$

    $9 \tan(37^{\circ})$

    $9 / \tan(37^{\circ})$

    $9 \cos(37^{\circ})$

20. A support cable runs from the top of a mast to a point 3 m from its base at a 52° angle. What is the mast’s height?

    $3 \sin(52^{\circ})$

    $3 \cos(52^{\circ})$

    $3 / \tan(52^{\circ})$

    $3 \tan(52^{\circ})$

Answer Sheet