Question

An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X = 60°

Answer 1

The length of awning which covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall, is 44.7 inches.

What is the law of sine?

The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

It can be given as,

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.

An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall.

The figure of the problem is attached below. The length of AB which is L has to be find out.

The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X = 60°. Thus, the angle ABC is 30 degrees.

$AB=90-60\\AB=30^o$

The sum of all the interior angle is 180 degree. Thus, the angle ACB is,

$\angle ACB=180-50-30\\\angle ACB=100^o$

Let suppose, the length of AB is a. Thus, by the sine law,

$\dfrac{\sin 30}{a}=\dfrac{\sin 100}{88}\\a=\dfrac{88\times\sin 300}{\sin 100}\\a=447\rm\; in$

Thus, the length of awning which covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall, is 44.7 inches.

Learn more about the sine law here;

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