Question

A 12 ft. ladder is leaning against a house. The ladder makes a 60° angle with the ground. Use special right triangles to find how far up the building the ladder will reach.

Answer 1

Given:

The length of the ladder  = 12 ft

The angle of ladder with ground = 60 degrees

To find:

How far up the building the ladder will reach.

Solution:

Using the given information draw a figure as shown below.

We need to find the vertical distance between the top of ladder and the ground.

Let x be the required distance.

In a right angle triangle,

$\sin \theta=\dfrac{Perpendicular}{Hypotenuse}$

In the below triangle ABC,

$\sin A=\dfrac{BC}{AC}$

$\sin 60^\circ=\dfrac{x}{12}$

$\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}$

Multiply both sides by 12.

$\dfrac{\sqrt{3}}{2}\times 12=x$

$6\sqrt{3}=x$

Therefore, the ladder will reach $6\sqrt{3}$ ft far up the building.