SOLUTION: A tree standing vertically on the side of the hill makes an angle of 115º with the side of the hill. At a point 68ft. down the slope, the tree subtends an angle of 22º. Find the he

Algebra ->  Trigonometry-basics -> SOLUTION: A tree standing vertically on the side of the hill makes an angle of 115º with the side of the hill. At a point 68ft. down the slope, the tree subtends an angle of 22º. Find the he      Log On


   

Question 1109680: A tree standing vertically on the side of the hill makes an angle of 115º with the side of the hill. At a point 68ft. down the slope, the tree subtends an angle of 22º. Find the height of the tree?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A tree standing vertically on the side of the hill makes an angle of 115º with the side of the hill.
At a point 68ft. down the slope, the tree subtends an angle of 22º.
Find the height of the tree?
:
Draw this out, the tree top and bottom and a point 68' down the hill form a triangle tbp
Let t = the top of the tree, b = the bottom of the tree, p = point 68' down from the tree
angle t = 22 degrees
angle b = 115 degrees
therefore 180 - 22 - 115 = 43 degrees = angle p
bp = 68ft
let x = the height of the tree. Use the law of sines
x%2Fsin%2843%29 = 68%2Fsin%2822%29
find the sines
x%2F.682 = 68%2F.3746
cross multiply
.3746x = 68 * .682
x = 46.376%2F.3746
x = 123.8 ft is the height of the tree