Question

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

Answer 1

The distance from the tree branch to the mouse is 30 feet.

Explanation:

Consider the provided information.

It is given that A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees.

The required figure is shown below:

As we know
`sin\theta =(opposite)/(hypotenuse)`

The opposite side of the angle 30 degrees is 15 ft and we need to find the value of hypotenuse.

Let hypotenuse is x.

Substitute the respective values in the above formula.

`sin(30) =(15)/(x)`

`(1)/(2) =(15)/(x)` (sin 30 = 1/2 )

`x=30`

Hence, the distance from the tree branch to the mouse is 30 feet.