This document contains information about trigonometric functions like sine, cosine, and tangent. It provides the values of these functions for various degree measurements from 0 to 90 degrees. It also includes example problems solving for unknown heights or distances using trigonometric ratios and the known angle of elevation or angle of observation for problems involving towers, lighthouses, and ships at sea. Solutions are provided for problems involving finding distances given angle of elevation measurements.

1. QA01 HEIGHT AND DISTANCE

3. 5 DECEMBER 09 3
What are different values of Sin?
Degrees :
0 30 45 60 90
take square root of : -
0/4 ¼ 2/4 ¾ 4/4
so Sin 30degree = ½ and sin 60 degree is
1.7/2 and sin 90 degree is 1. Sin 45 = 1/1.4
(square root of 2/4) answer
the same value repeat from 180 degree to
270 degree

4. 5 DECEMBER 09 4
What are different values of Cos?

5. 5 DECEMBER 09 5
What are different values of Tan?
Degrees :
0 30 45 60 90
divide sin values by cos values
0/1 1/1.73 1 1.7 Infinite

8. A.30 B.45 C.60 D.90
Option A
Let AB be the tree and AC be its shadow.
Let ACB = θ
= 30

9. 5. From a point P on a level ground, the angle of elevation of
the top tower is 300 whose height is 100m.
Find the distance between P and the foot of the tower.
A. 149m B.156m C.173m D.200m
Let AB be the tower.
Then /APB =300 and AB = 100m
= 100 x 1.732
= 173 m

10. A.21.6 m B. 23.2 m C. 24.72 m D.None of these
Let AB be the observer and CD be the tower.
Then, CE = AB = 1.6 m,
CD = CE + DE = (1.6 + 20) m = 21.6 m.

11. 2)A man standing at a point P is watching the top of a
tower, which makes an angle of elevation of 300 and after
moving towards the tower the angle of elevation becomes 600
.What is the distance between the base of the tower and the
point P?
A.43 units B.8 units C.12 units
D. Data inadequate One of AB, AD and CD should be given.

12. 3. The angle of elevation of a ladder leaning against a wall is
600 and the distance from the wall to the foot of the ladder is
4.6 m. The length of the ladder is
A.2.3 m B.4.6 m C.7.8 m D.9.2 m
Let AB be the wall and BC be the ladder.
Then /ACB = 600 and AC = 4.6m.
 BC = 2 X AC
= 2 X 4.6 m
= 9.2 m

13. 1. Two ships are sailing in the sea on the two sides of a lighthouse.
The angle of elevation of the top of the lighthouse is observed
from the ships are 300 and 450. If the height of the light house is
100m then the distance between the two ships are
A.173 m B.200 m C.273 m D.300 m
Let AB be the lighthouse and C and D be the positions of the
ships.
Then, AB = 100 m, ACB = 30º and ADB = 45º
= (100 X 2.73) m
= 273 m