# Mrs. O'Leary's cat is stuck in her backyard tree. A fireman positions a ladder against the tree branch and rescues the cat.?

## Mrs. O'Leary's cat is stuck in her backyard tree. A fireman positions a ladder against the tree branch and rescues the cat. The ladder was extended to 22 feet, and made an angle of 62 degrees with the ground. What was the cat's vertical height in the tree. Use picture please and include if it SOH, CAH, TOA in it!

Jun 8, 2018

$B C = \sin \left({62}^{\circ}\right) \cdot 22 \approx 19.42$

#### Explanation:

A good idea is always to draw a sketch

The important thing to notice is the right angled triangle

We want to find the cats height, i.e. the length color(blue)(BC (Opposite side)

We know the angle color(blue)(A=62^@ and the hypotenuse color(blue)(AC=22

So we need to use sine (SOH)

$\sin \left(A\right) = \text{Opposite"/"Hypotenuse}$

$\implies \text{Opposite"=sin(A)*"Hypotenuse}$

Substituting the values

$B C = \sin \left({62}^{\circ}\right) \cdot 22 \approx 19.42$