Question

Sam the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. How far away is Sam from the bird? Round the answer to the nearest hundredth.

Answer 1

Answer:

24.59 feet

Step-by-step explanation:

Let x represent the distance between Sam and the bird.

We have been given that am the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. We are asked to find the distance between Sam and the bird.

We can see from our attachment that Sam, the bird and angle of depression forms a right triangle with respect to ground. We can see that side 10 ft is opposite side and and side x is hypotenuse for the 24 degree angle.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(24^{\circ})=\frac{10}{x}$

$x=\frac{10}{\text{sin}(24^{\circ})}$

$x=\frac{10}{0.406736643076}$

$x=24.5859333557$

$x\approx 24.59$

Therefore, the bird is approximately 24.59 feet away from Sam.