32. The shadow of a lagstaff is three times as long as the shadow of t

1.	32. The shadow of a lagstaff is three times as long as the shadow of the flagstaff when the sun rayseet the ground at an angle of 60. Find the angle between the sun rays and the ground at thetime of longer shadow.
Answer» Here, AB is the flag staff, C is the end point of the shadow when the angle of elevation is 60°, andθis the angle at which we need to find. Let AB =x, BC =y By given condition, BD = 3y In rightΔABC,ABBC= tan 60⁰xy=3x = √3 yIn right ΔABD,ABBD=tanθx3y=tanθ3y3y=tanθ1/√3=tanθθ = 30° [tan 30° =1/√3]Thus, the required angle is 30°.

32. The shadow of a lagstaff is three times as long as the shadow of the flagstaff when the sun rayseet the ground at an angle of 60. Find the angle between the sun rays and the ground at thetime of longer shadow.

Answer»

Here, AB is the flag staff, C is the end point of the shadow when the angle of elevation is 60°, andθis the angle at which we need to find.

Let AB =x, BC =y

By given condition, BD = 3y

In rightΔABC,ABBC= tan 60⁰xy=3x = √3 yIn right ΔABD,ABBD=tanθx3y=tanθ3y3y=tanθ1/√3=tanθθ = 30° [tan 30° =1/√3]Thus, the required angle is 30°.