Use tables of trigonometric ratios to answer the following:

1. Use tables of trigonometric ratios to find each of the following:

• (a) sin 60°
• (b) cos 28° 28′
• (c) tan 63° 48′

2. Use tables of trigonometric ratios to find the value of r in each of the following:

• (a) tan r = 0.9036
• (b) cos y = 0.2554
• (c) sin y = 0.4971

3. In the following figure, find the values of x and α.

4. A pendulum consists of a bob hanging at the end of a string which is 18 cm long. Find the vertical height through which the bob rises and falls as the pendulum swings through 30° on each side of the vertical.

5. When the angle of elevation of the sun is 30°, the shadow of a post 6 m long is cast. When the angle of elevation is 60°, find the height of a post.

6. The angle of elevation of the top of a church tower from a point due East of it and 96 m away from its base is 30°. From another point due West of the church tower the angle of elevation of the top is 60°. Find the distance of the later point from the base of the church tower.

7. Point A is 289 m from point C on a bearing N32°W, point B is 450 m from C on a bearing N88°E. Find the distance from A to B.

8. When the angle of elevation of the sun is 55°, a tower casts a shadow 20 m long. Find the height of the tower.

9. A kite is flying directly over a straight path 100 m long. The angle of elevation of the kite at one end of the path is 35°, if the angle of elevation of the kite at the other end of the path is 55°, how high is the kite?

10. A boy stands 25 m away from the foot of a tree and observes that from a point on the ground the angle of elevation of the top of the tree is 30° closer to the foot of the tree. The angle of elevation of the top is now 50°. How high is the tree?

11. Find the value of each unknown quantity shown in the following figures:

12. An observer is at point A on the bank of a river. The foot of a coconut tree is at point P directly across on the opposite bank. A distance AB of 27 m is measured along the bank so that ∠BAP is a right angle and ∠ABP = 42°, as shown in the following figure.

Find the following:

1. The width of the river.
2. The height of a coconut tree if the angle of elevation of the top of the coconut tree is 22° from A.
3. The angle of elevation of the top of the coconut tree from B.
4. The distance from B to the top of the coconut tree.

13. A ladder of length 12 m is set against a vertical wall.

(a) If it makes an angle of 28° with the wall, how far up the wall does it reach?

(b) If it reaches 10 m up the wall, what angle does it make with the horizontal?