Tricky Height !!!!!

Geometry Level 2

From the top of a 7-meter-high building, the angle of elevation of the top of a cable tower is 60 ° 60° and the angle of depression of its foot is 45 ° . 45°. Determine the height of the tower in meters.


The answer is 19.12.

Karan Ahire by Karan Ahire , 21, India

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1 solution

Rishik Jain
Mar 7, 2016

Given: A B = 7 m tan ⁡ 4 5 ∘ = D C A C ⟹ A C = D C A B = A C = D C = 7 m tan ⁡ 6 0 ∘ = E C A C ⟹ E C = 7 × 3 ∴ The height of the tower is E C + D C ⟹ 7 3 m + 7 m = 19.124 m \textbf{Given: } AB=7 m \\ \tan 45^{\circ}=\frac{DC}{AC} \implies AC=DC\\AB=AC=DC=7 m \\ \tan 60^{\circ}=\frac{EC}{AC} \implies EC= 7 \times \sqrt{3} \\ \therefore \textbf{The height of the tower is }EC + DC \\ \implies 7\sqrt{3}m+7m=\large \boxed{19.124 m}

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