Question

The length of the shadow of a pole on level ground increases by 90 metres when the angle of elevation of the sun changes from 58 degrees to 36 degrees. calculate and correct to three s.f , the height of the pole​

Answer 1

120 m

Explanation:

Let the length of the pole be a and the shadow be b at 58° and b+90 at 36°.

Then, as the pole and its shadow form a right triangle, we have:

• a/b = tan (58°)

• a/(b+90) = tan (36°)

As,

• tan (58°) ≈ 1.6
• tan (36°) ≈ 0.727

The equations change to:

• a = 1.6b
• a = 0.727 (b+90)

Comparing the two equations:

• 1.6b = 0.727b + 0.727*90
• 1.6b - 0.727b = 65.43
• 0.873b = 65.43
• b = 65.43/0.873
• b ≈ 75

Then

• a = 1.6b = 1.6*75 = 120 m