Question

THE ANGLE OF ELEVATION OF THE TOP OF A TREE FROM A POINT P TO THE GROUND IS 30 DEGREES. FROM A POINT Q, 10 METERS CLOSER TO THE FOOT OF THE TREE THE ANGLE OF ELEVATION IS 45 DEGREES. HOW TALL IS THE TREE?

Answer 1

The tree is 6.19 metres tall

Explanation:

Tan 45° = H/10

H = 10 (Tan45°)... let this be the first equation

Let the distance between Q and P be X

Tan 30° = H/(10 + X)

H = Tan30° (10 + X)...let this be equation 2

But H = H,

so 10 (Tan45°) = Tan30° (10 + X)

10 (1) = 0.5774 (10 + X)

10 = 5.774 + 0.5774X

(10 - 5.774) = 0.5774X

4.226 = 0.5774X

X = 0.73

So H will be :

H = Tan30° (10 + X)

H = 0.5773 (10 + 0.73)

H = 6.19m