107th Problem 2016

Geometry Level 2

The angle of elevation from a point 118 feet from the base of a tower to the top of the tower is 69. 8 ∘ 69.8^\circ .

What is the approximate height (in feet) of the tower?

Round the answer to two decimal places.

Check out the set: 2016 Problems .


The answer is 320.71.

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Ashish Menon
Apr 24, 2016

The figure given forms a right-angled triangle.
Applying the formula:-
tan ⁡ θ \tan \theta = Perpendicular Base \dfrac{\text{Perpendicular}}{\text{Base}}
tan ⁡ 69.8 ° = ? 118 \tan 69.8° = \dfrac{?}{118}
2.717 = ? 118 2.717 = \dfrac{?}{118}
? = 2.717 × 118 ≈ 320.71 ? = 2.717 × 118 \approx \boxed{320.71} metres.

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