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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

Question 1.

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height 10\(\sqrt{3}\) m.

Solution:

Question 2.

A road is flanked on either side by continuous rows of houses of height 4\(\sqrt{3}\) m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30°. Find the width of the road.

Solution:

Question 3.

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? (\(\sqrt{3}\) = 1.732)

Solution:

Let ‘H’ be the fit of the window. Given that elevation of top of the window is 60°.

Given that elevation of bottom of the window is 45°.

∴ Height of the window = 3.66 m

Question 4.

A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 40°. Find the height of the pedestal. (tan 40° = 0.8391, \(\sqrt{3}\) = 1.732)

Solution:

Let ‘p’ be the fit of the pedestal and d be the distance of statue from point of cabs, on the ground.

Given the elevation of top of the statue from p^{f} on ground is 60°.

Question 5.

A flag pole ‘h’ metres is on the top of the hemispherical dome of radius V metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find

(i) the height of the pole

(ii) radius of the dome.

Solution:

Question 6.

The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

Solution:

Let BD be tower of height = 15 m

AE be pole of height = ‘p’

Question 7.

A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 25 m away from the base of the pole, what is the height of the pole?

Solution:

This mile calculator estimates the number of driving miles between two locations in the United States.

Question 8.

A traveler approaches a mountain on highway. He measures the angle of elevation to the peak at each milestone. At two consecutive milestones the angles measured are 4° and 8°. What is the height of the peak if the distance between consecutive milestones is 1 mile, (tan 4° = 0.0699, tan 8° = 0.1405).

Solution: