# Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.4

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.4

Question 1.
From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree. ($$\sqrt{3}$$ = 1.732)
Solution:

Question 2.
A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill. ($$\sqrt{3}$$ = 1.732)
Solution:

∴ The height of the hill = 120 + 40 = 160 m
The distance of the hill from the ship is AC = x = $$40 \sqrt{3}$$ m = 69.28 m

Question 3.
If the angle of elevation of a cloud from a point ‘h’ metres above a lake is θ1 and the angle of depression of its reflection in the lake is θ2. Prove that the height that the cloud is located from the ground is $$\frac{h\left(\tan \theta_{1}+\tan \theta_{2}\right)}{\tan \theta_{2}-\tan \theta_{1}}$$
Solution:

Let AB be the surface of the lake and let p be the point of observation such that AP = h meters.
Let C be the position of the cloud and C’ be its reflection in the lake. Then CB = C’B.
Let PM be ⊥r from P on CB
Then ∠CPM = θ1, and ∠MPC = θ2
Let CM = x.
Then CB = CM + MB = CM + PA
= x + h

Hence proved

Question 4.
The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.
Solution:

Since 150m > 120m, yes the height of the above mentioned tower meet the radiation norms.

Question 5.
The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 600 and 30° respectively. Find
(i) The height of the lamp post.
(ii) The difference between height of the lamp post and the apartment.
(iii) The distance between the lamp post and the apartment. ($$\sqrt{3}$$ = 1.732)
Solution:

= 114.312 m

Question 6.
Three villagers A, B and C can see each T other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30° . Calculate :

(i) the vertical height between A and B.
(ii) the vertical height between B and C. (tan20° = 0.3640, $$\sqrt{3}$$ = 1.732)
Solution: