Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

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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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 1
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 2

Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 3
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 4

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 5
Let ‘H’ be the fit of the window. Given that elevation of top of the window is 60°.
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 6
Given that elevation of bottom of the window is 45°.
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 7
∴ Height of the window = 3.66 m

Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 8
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 pf on ground is 60°.
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 9

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 10

Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 11
Let BD be tower of height = 15 m
AE be pole of height = ‘p’
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 12
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 13

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 14
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 15

Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

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:
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 16
Samacheer Kalvi 10th Maths Chapter 6 Trigonometry Ex 6.2 17

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