Question

The diagram shows an awning on the front of a building. The top of the awning makes a 40° angle with the building. The base of the awning is 8 feet from the building. What is the height of the awning? Round to the nearest tenth if necessary.

Answer 1

Height of the awning = 9.52 feet

Explanation:

For better understanding of the solution, see the attached diagram of the problem :

According to the figure, AB is the height of the awning

Now, the base of awning will be perpendicular to the building

⇒ m∠ABC = 90°

In ΔABC, By using angle sum property of a triangle

m∠ABC + m∠ACB + m∠BAC = 180°

⇒ m∠ACB = 50°

`Now,\tan 50=(Perpendicular)/(Base)\\\\tan 50=(AB)/(8)\\\\\implies AB=8* \tan 50\\\\\bf\implies AB=9.52 \textbf{ feet}`

Hence, Height of the awning = 9.52 feet