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Class 10 Maths Extra Questions for Application of Trigonometry




Question 1.
The angle of elevation of a cloud from point h meter above a lake is α. The angle of depression of its reflection in the lake is 45°. Find the height of the cloud

Question 2.
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 300 with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree

Question 3
The shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 60° to 45°, what is the height of the building?

Question 4
An air plane, flying horizontally 1000 m above the ground, is observed at an angle of elevation 60° from a point on the ground. After a flight of 10 seconds, the angle of elevation at the point of observation changes to 30°. Find the speed of the plane in m/s.

Question 5
From the top of a h meters high building, the angle of depression to the bottom of a second building is 30 degrees. From the same point, the angle of elevation to the top of the second building is 45 degrees. Calculate the height of the second building.

Question 6
From the top of a building 60 m high, the angels of depression of the top and bottom of a vertical lamp post are observed to be 30° and 60°respectively. Find
(i) horizontal distance between the building and the lamp post
(ii) height of the lamp post.

Question 7
The angle of depression of two war ships from the top of the light house are 45° and 30° towards west. The war ships are 500 m apart. Find the height of the lighthouse

Question 8
At the foot of a mountain the elevation of its summit is 45°. After ascending 1000 m towards the mountain up a slope of 30° inclinations, the elevation is found to be 60°. Find the height of the mountain

Question 9
The angle of elevation of a jet fighter from point A on the ground is 60 degrees. After 15 seconds the angle of elevation changes from 60 degrees to 30 degrees. If the jet is flying at a speed of 720 km/hr., find the height at which the jet fighter is flying.

Question 10
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a Truck at an angle of depression of 30°, which is approaching the foot of tower with a uniform speed. Six minutes later, the angle of depression of the truck is found to be 60°. Find the time taken by the truck to reach the foot of the tower


Answer
(1) h tan(45+α)
(2) 8√3
(4) 240√3 km/h
(6) 34.64m h=40m
(8) $500(1+ \sqrt {3})$ m
(9) $1500 \sqrt {3}$
(10) 3min
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Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20