Trigonometry (C10)
Trigonometric ratios; Relationships between the ratios; Trigonometric identities; Heights and Distances
Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m
Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.
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A, B, C are interior angles of ΔABC. Prove that cosec (A+B)/2 = sec C/2
A, B, C are interior angles of ΔABC. Prove that cosec (A+B)/2 = sec C/2
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If sin (A + 2B) = √3/2 and cos (A + 4B) = 0, A > B
If sin (A + 2B) = √3/2 and cos (A + 4B) = 0, A > B, and A + 4B ≤ 90º, then find A and B.
Read more …Two poles of equal heights are standing opposite to each other
Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point in between them on the road, the angles of elevation of the top of poles are 60º and 30º respectively. Find the height of the poles and the distances of the point from the poles.
Read more …If sin θ + cos θ = √2, then evaluate: tan θ + cot θ
If sin θ + cos θ = √2, then evaluate: tan θ + cot θ
Read more …The angle of elevation of the top of a hill at the foot of a tower is 60º
The angle of elevation of the top of a hill at the foot of a tower is 60º and the angle of depression from the top of tower to the foot of hill is 30º. If tower is 50 metre high, find the height of the hill.
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If tan 2A = cot (A - 18°), where 2A is an acute angle
If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.
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As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships
As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3 = 1.732]
Read more …The angles of depression of the top and bottom of a building 50 metres high
The angles of depression of the top and bottom of a building 50 metres high as observed from the top of a tower are 30° and 60°, respectively. Find the height of the tower and also the horizontal distance between the building and the tower.
Read more …An aeroplane is flying at a height of 300 m above the ground
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3 = 1.732]
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