This page 10th samacheer kalvi math solution for exercise 7.2 part 5 is going to provide you solution for every problems that you find in the exercise no 7.2

**Question 13 :**

A boy standing on the ground, spots a balloon moving with the wind in a horizontal line at a constant height . The angle of elevation of the balloon from the boy at an instant is 60°. After 2 minutes, from the same point of observation,the angle of elevation reduces to 30°. If the speed of wind is 29√3 m/min. then, find the height of the balloon from the ground level.

**Solution :**

Distance covered by the balloon = BC

BC = Time x Speed ==> 2 x 29 √3 ==> 58√3 m

AB = x then AC = x + 58√3

In triangle DAC :

∠DAC = 30°

tan θ = opposite side/Adjacent side

tan 30° = DC/AC

1/√3 = DC/(x + 58√3)

DC = (x + 58√3)/√3 ----(1)

In triangle EAB :

∠EAB = 60°

tan θ = opposite side/Adjacent side

tan 60° = EB/AB

√3 = EB/x

x√3 = EB

EB = √3x ---->(2)

Since EB = DC

(1) = (2)

(x + 58√3)/√3 = √3x

x + 58√3 = 3x

3x - x = 58√3

2x = 58√3

x = 58√3/2 ==> 29√3 m

Height of the balloon from ground level EB = √3 x

= 29 √3 (√3)

= 29(3) ==> 87 m

Hence height of the balloon from ground level = 87 m.

**Question 14 :**

A straight highway leads to the foot of a tower . A man standing on the top of the tower spots a van at an angle of depression of 30°. The van is approaching the tower with a uniform speed. After 6 minutes, the angle of depression of the van is found to be 60°. How many more minutes will it take for the van to reach the tower?

**Solution :**

From the given information, we can draw a rough diagram

Distance covered by the van to reach D from C = 6 minutes

time taken = x

Distance between D and C = 6x

In triangle ACB

∠ACB = 30°

tan θ = opposite side/Adjacent side

tan 30° = AB/BC

1/√3 = AB/(BD+DC)

1/√3 = AB/(BD+6x)

(BD+6x)/√3 = AB ----(1)

In triangle ABD

∠ABD = 60°

tan θ = opposite side/Adjacent side

tan 60° = AB/BD

√3 = AB/BD ==> AB = BD√3 -----(2)

(1) = (2)

(BD+6x)/√3 = BD√3

BD + 6x = BD(3)

3BD - BD = 6x

2BD = 6x

BD = 6x /2 = 3x

Here 3 represents number of minutes covered by the van and x stands for time taken.

Hence 3 more minutes will it take for the van to reach the tower.

After having gone through the stuff given above, we hope that the students would have understood "10th samacheer kalvi math solution for exercise 7.2 part 3".

Apart from the stuff given above, if you want to know more about "10th samacheer kalvi math solution for exercise 7.2 part 3", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...