Question

An 18-foot ladder is leaning against the side of a building such that its base makes an angle of 65º with the ground. How far from the side of the building, b, should the base of the ladder be placed? Round to the nearest tenth of a foot.

Answer 1

Hello!

This problem is about relating trigonometric values to an unknown side.

We are given an angle side, and we can determine that another angle made would be a 90 degree angle.

Meaning we could solve for the third unknown angle by knowing that the interior angles of a triangle add up to 180 degrees.

$65+90+x+180$

$x=180-90-65$

$x=25$

After knowing this, we could use the law of sines, which states that the ratio of a side and the sin of its opposite angle are equal to any other ratio.

$\frac{16}{sin(90)}=\frac{b}{sin(25)}$

$b=16sin(25)$

Make sure to be in degrees when putting this in a calculator.

$b=6.8$

Hope this helps!