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Introduction to Trignometry & its Equation

The  angle  of  elevation  of  the  top  of  a  tower  from  certain  point  is  30°.  If  the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Introduction to Trignometry & its Equation

From a balloon vertically above a straight road, the angles of depression of two cars at an instant are found to be 45° and 60°.  If the cars are 100 m apart, find the height of the balloon.

Introduction to Trignometry & its Equation

A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, find the height of the centre of the balloon.

Introduction to Trignometry & its Equation

Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ.

Introduction to Trignometry & its Equation

An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine  the  angle  of  elevation  of  the  top  of  the  tower  from  the  eye  of  the observer.

Introduction to Trignometry & its Equation

 If 2sin²θ – cos²θ = 2, then find the value of θ.

Introduction to Trignometry & its Equation

 Simplify (1 + tan2θ) (1 – sinθ) (1 + sinθ)

Introduction to Trignometry & its Equation

A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

Introduction to Trignometry & its Equation

Prove that sin⁶θ + cos⁶θ + 3sin²θ cos²θ = 1

Introduction to Trignometry & its Equation

Write ‘True’ or ‘False’ and justify your answer.

If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.