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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (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

tan%2830%29=opposite%2Fadjacent=x%2F180


tan%2830%29=x%2F180 Start with the given equation.


sqrt%283%29%2F3=x%2F180 Take the tangent of 30 to get sqrt%283%29%2F3


180%2Asqrt%283%29=3x Cross multiply


%28180%2Asqrt%283%29%29%2F3=x Divide both sides by 3 to isolate x.


60%2Asqrt%283%29=x Reduce


60%2A1.732=x Evaluate the square root of 3


103.92=x Multiply


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

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Answer:

So to the nearest foot, the tree is about 104 ft high.