Question

when the angle of elevation of the sum is 30,the length of the shadow of a tower is 90m. Find the height of the tower.

Answer 1

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Answer 2

Draw the figure as described :

• Draw a right angled triangle ABC right angled at B.
• Length of the shadow is BC at the bottom
• Mark BC as 90 m
• The angle of elevation is 30°
• Mark ∠ACB as 30°

Now we know that :

tan ∅ = height/base

Let the height of the tower be h.

tan 30° = h / 90 m

==> 1 / √3 = h / 90 m

==> h = 90 / √3 m

==> h = 90 / √3 × √3 / √3  m

==> h = 90√3 / 3 m

==> h = 30 √3 m

Take √3 as 1.73

==> h = 30√3

==> h = 30 ×1.73

==> h = 51.9 m

The height of the tower is 51.9 m

Hope it helps you

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