# KSEEB Solutions for Class 10 Maths Chapter 12 Some Applications of Trigonometry Additional Questions

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## Karnataka State Syllabus Class 10 Maths Chapter 12 Some Applications of Trigonometry Additional Questions

I. Multiple Choice Questions:

Question 1.
The angle of elevation of the top of a tower from a point at a distance of 100 m from the base of the tower is found to be 45° then height of the tower is
a. 50 m
b. 100m
c. 50$$\sqrt{2}$$ m
d. 50$$\sqrt{2}$$ m
b. 100m

Question 2.
Find the angle of elevation of the top of a tower, whose height is 100 m, at a point whose distance from the base of the tower is 100 m.
a. 30°
b. 60°
c. 45°
d. 90°
c. 45°

Question 3.
The angle of elevation of the top of tree from a point at a distance of 200 m from its base is 60° the height of the tree is
a. 50$$\sqrt{3}$$m
b. 100$$\sqrt{3}$$ m
c. 200$$\sqrt{3}$$m
d. $$\frac{200}{\sqrt{3}}$$ m
c. 200$$\sqrt{3}$$m

Question 4.
Find the length of the shadow of 10 m high tree of the angle of elevation of the sun is 30°
a. 10 m
b. $$\frac{10}{\sqrt{3}}$$ m
c. 10$$\sqrt{3}$$m
d. 20 m
d. 20 m

Question 5.
If the shadow of 10 m high tree is 10$$\sqrt{3}$$m then find the angle of elevation of the sun
a. 60°
b. 90°
c. 45°
d. 30°
c. 45°

Question 6.
The ratio of the length of a tree and its shadow is 1 : $$\frac{1}{\sqrt{3}}$$. The angle of the sun’s elevation is
a. 30°
b. 45°
c. 60°
d. 90°
c. 60°

Question 7.
The ratio of the length of a rod to its shadow is 1: $$\sqrt{3}$$. The angle of elevation of the sun is
a. 30°
b. 60°
c. 45°
d. 90°
a. 30°

Question 8.
If the angle of elevation of the sun is 45°, then find the length of the shadow of a tower whose height is ‘h’m
a. $$\frac{h}{2}$$ m
b. h m
c. 2h m
d. h$$\sqrt{3}$$ m
b. h m

Question 9.
The angle of elevation of the sun is 45°. Then, the length of the shadow of a 12 m high tree is
a. 6$$\sqrt{3}$$ m
b. 12$$\sqrt{3}$$ m
c. $$\frac{12}{\sqrt{3}}$$ m
d. 12 m
d. 12 m

Question 10.
From a bridge, 25 m high, the angle of depression of a boat is 45°. Find the horizontal distance of the boat from the bridge.
a. 25 m
b. $$\frac{25}{2}$$
c. 50 m
d. 25$$\sqrt{3}$$ m
a. 25 m

Question 11.
If the angle of elevation of the sun is top 60°, then find the ratio of the height of a tree with its shadow.
a. $$\sqrt{3}$$ : 1
b. 1 : $$\sqrt{3}$$
c. 3 : 1
d. 1 : 3
a. $$\sqrt{3}$$ : 1

Question 1.
The angle of elevation of an aeroplane from a point on the ground is 45°. After a flight of 15 seconds horizontally, the angle of elevation changes to 30° if the aeroplane is flying at a constant height of 2500 m then find the speed of the plane.

2500 + BD = 2500$$\sqrt{3}$$
BD = 2500$$\sqrt{3}$$ – 2500
BD = 2500($$\sqrt{3}$$ – 1)m
But BD = CE = 2500 ($$\sqrt{3}$$ – 1) m

Speed = 118.33.m / sec

Question 2.
From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of a tower is 30° the angle of elevation of the top of water tank on top of the tower is 45°. Find
(i) height of the tower
(ii) depth of the tank

∴ CD = AD – AC = 40 – $$\frac{40}{\sqrt{3}}$$
CD = 40$$\left(1-\frac{1}{\sqrt{3}}\right)$$ m

Question 3.
A tall building casts a shadow of 300 m long when the sun’s altitude elevation is 30°. Find the height of the tower.

= 100$$\sqrt{3}$$ m
Height of the tower is 100$$\sqrt{3}$$ m

Question 4.
A tree is broken over by the wind forms a right angled triangle with the ground. If the broken parts makes an angle of 60° with the ground and the top of the tree is now 20 m from its base, how tall was the tree.

AB = 20$$\sqrt{3}$$ m.
Height of tree = AD = AB + BC
= 40 + 20$$\sqrt{3}$$
= 20(2 + $$\sqrt{3}$$)

Question 5.
The angle of elevation of the top of a flag post from a point on a horizontal ground is found to be 30°. On walking 6 m towards the post, the elevation increases by 15°.
Find the height of the flag post.

In ∆ ABC θ = 30°.

Y + 6 = x$$\sqrt{3}$$ → (1)
In ∆ ABD, θ = 45°

x = y → (2)
Put equation (2) in equation (1)

Question 6.
From the top of a building 16 m high, the angular elevation of the top of a hill is 60° and the angular depression of the foot of the hill is 30°. Find the height of the hill.

In ∆ AED, θ = 30°

In ∆ BCE, θ = 60°

From (1) and (2)

16 × 3 = x – 16
x = 48 + 16 = 64
∴ The height of the hill is 64 m.

Question 7.
Two windmills of height 50 m and 40 m are on either side of the field. A person observes the top of the windmills from a point in between the towers. The angle of elevation was found to be 45° in both the cases. Find the distance between the windmills.