Wavy windows on the building!

Geometry Level pending

From a point 10m away from the building, the angles of elevation of the top and bottom of a window are of measure 30° and 45°, respectively. How tall is the window ?

Please note that the building is perpendicular to the ground.

Hint: You may use a diagram to help


The answer is 4.23.

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Here I have made a simple diagram:

Let C and D denote the bottom and top of the window; and A is the point 10 m away from the building. We have to find the length of CD. Let us consider the triangle ABC.

t a n 30 ° = l B C 10 tan 30° = \frac{lBC}{10}

B C = 10 t a n 30 ° BC = 10 tan 30°

= 10 ∗ = 10 * 1 √ 3 \frac{1}{√3}

= 5.77 m = 5.77 m

Again consider the triangle ABD in which:

tan 45° = B D 10 \frac{BD}{10}

BD = 10 tan 45°

= 10 * 1 = 10m

Hence, CD = BD - BC

= 10 - 5.77

= 4.23

So the height of the window is 4.23m

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