A 12 foot ladder is leaning against a wall. The angle of elevation is 23 degrees. How far away from the wall is the ladder?

Question

A 12 foot ladder is leaning against a wall. The angle of elevation is 23 degrees. How far away from the wall is the ladder?

Answer 1

Brett, we can use the law of sines. Since we have the angle of elevation and assume the wall makes a right angle with the ground, our angle opposite the ground is 180 - (90 + 23) = 67

 

12/sin90º = b/sin67º

 

12sin67º = bsin90º

b = 12sin67º/sin90º

 

Throw the right side into your calculator for your answer!

Answer 2

Hi Brett,

The ladder makes a right triangle with the wall it's leaning against. The ladders length, 12 ft is the hypotenuse. The vertical side of the right triangle is the distance away from the wall. It's adjacent to the given angle of elevation, so use the Cosine function.

 

Cos(Θ) = Adj / Hyp

 

Cos(23º) = x / 12

 

12*Cos(23º) = x