SOLUTION: A ranger spots a forest fire while standing on a 24-meter observation tower. The angle of depression from the tower to the fire is 30 degrees. To the nearest meter, how far is the

Question 770889: A ranger spots a forest fire while standing on a 24-meter observation tower. The angle of depression from the tower to the fire is 30 degrees. To the nearest meter, how far is the fire from the base of the tower? Is the answer 41.56?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A ranger spots a forest fire while standing on a 24-meter observation tower. The angle of depression from the tower to the fire is 30 degrees. To the nearest meter, how far is the fire from the base of the tower? Is the answer 41.56?
-----
Draw the picture.
You have a right triangle with base angle = 30 degrees and height = 24 meters.
----
Find the base.
tan(30) = height/base
----
base = height/tan(30) = 24/tan(30) = 4.57 meters
=============================================
You are correct.
====================
Cheers,
Stan H.
=================
RELATED QUESTIONS
A ranger spots a forest fire while on a 40-meter observation tower. The angle of... (answered by Alan3354)

A ranger spots a forest fire while on a 45-meter observation tower. The angle of... (answered by vertciel)

A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower (answered by stanbon)

A forest ranger spots a fire from a 28-foot tower. The angle of depression from the tower (answered by fractalier)

As a forest ranger you are in lookout tower in a forest. Your observation position is... (answered by mananth)

From the top of a fire tower, a forest ranger sees his partner on the ground at an angle... (answered by josgarithmetic,ikleyn,math_tutor2020)

From the top of a 45 ft. fire tower, a forest ranger sees his partner on the ground at an (answered by ikleyn)

I need help with the following question please. A ranger in a fire tower A spots a... (answered by Alan3354)