SOLUTION: A forester, 180 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is 30�. Estimate the height of the tree to the nearest tent

Question 177266This question is from textbook
: A forester, 180 feet from the base of a redwood tree, observes that the angle between the ground and the top of the tree is 30�. Estimate the height of the tree to the nearest tenth of a foot. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you draw the triangle, you'll find that we need to find the opposite side given the angle 30 degrees and the adjacent side 180

So we can use the tangent function

Start with the given equation.

Take the tangent of 30 to get

Cross multiply

Divide both sides by 3 to isolate x.

Reduce

Evaluate the square root of 3

Multiply

So the answer is which means that the tree is about 103.92 ft high

=======================================

Answer:

So to the nearest foot, the tree is about 104 ft high.
RELATED QUESTIONS
Solve and show all work, please. Thanks! A forester is 50 m from the base of a tree... (answered by venugopalramana)

A forester is estimating the amount of lumber contained in a tree. When she stands 35... (answered by Cromlix)

Angles of Depression/Elevation: From the top of a tower 83 feet high, a man observes that (answered by lynnlo)

Angles of Depression/Elevation: From the top of a tower 83 feet high, a man observes that (answered by mananth)

a gaint redwood tree fell during a storm. the place where the tree craacked is 28 feet... (answered by bobdabuildr)

John wants to measure the height of a tree. He walks exactly 100 feet from the base of... (answered by mananth)

From a point on level ground 60 feet from the base of a tree, the angle between the... (answered by ewatrrr,nyc_function)

A student stands 29 m away from the foot of a tree and observes that the angle of... (answered by Solver92311,mananth,ikleyn)

A 15 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a... (answered by ikleyn)