Question

if a fire ranger on a tower 150 ft spot a fire at an angle of 30-depression, how many feet away is the tower is from the fire.

Answer 1

By using trigonometric relations, we will see that the distance to the fire is .173.21 ft

How to find the distance to the fire?

Here we can compare this with a right triangle. We know that one angle on the right triangle is 30°, and the adjacent cathetus to that triangle is 150ft.

Now, we want to find the hypotenuse of said triangle, which is the distance to the fire.

So we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Replacing what we know, we get:

cos(30°) = 150ft/hypotenuse

hypotenuse = 150ft/cos(30°) = 173.21 ft

So the distance to the fire is 173.21 ft

If you want to learn more about right triangles:

https://brainly.com/question/2217700

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