SOLUTION: dave is trying to measure the height of a pine tree in baguio. at a certain point on the same level ground as the base of the tree, he finds that the angle of elevation to the top

Algebra ->  Trigonometry-basics -> SOLUTION: dave is trying to measure the height of a pine tree in baguio. at a certain point on the same level ground as the base of the tree, he finds that the angle of elevation to the top       Log On


   

Question 932071: dave is trying to measure the height of a pine tree in baguio. at a certain point on the same level ground as the base of the tree, he finds that the angle of elevation to the top of the tree is 48degree. Moving to a point 17ft farther, the angle of elevation becomes 36degree. find the height of the tree..
Sir/Maam i need this today because i have a lot of homework and i cant answer this because i cant understand. Im so thankful who can answer this.. GODBLESS...
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Draw right triangle and mark a point 17ft farther from the tree b,the height of the tree h, angle off 36° between horizontal line and sloping line mark with theta.
Then:

the angle of elevation to the top of the tree was 48°. Moving to a point 17ft farther, the angle of elevation becomes 36°.
h=height
h=hight
b=base=xft
%28theta%29=48°
tan%28theta%29=h%2Fx
x=h%2Ftan%28theta%29
x=h%2Ftan%2848%29
x=h%2F1.1106
h=1.1106x...........eq.1
Moving to a point 17ft farther, the angle of elevation becomes 36,° so we have:
b=base=xft%2B17ft
%28theta%29=36°
tan%28theta%29=h%2F%28x%2B17ft%29
h=%28x%2B17ft%29tan%28theta%29
h=x%2Atan%2836%29%2B17ft%2Atan%2836%29
h=0.72654x%2B17ft%2A0.72654
h=0.72654x%2B12.35118ft...........eq.2....
the left sides of eq.1=eq.2, so we have
1.1106x=0.72654x%2B12.35118ft...........solve for h
1.1106x-0.72654x=12.35118ft
0.38406x=12.35118ft
x=12.35118ft%2F0.38406
x=32.16ft
=> b=base=xft%2B17ft=> b=32.16ft%2B17ft=49ft
h=49.16ft%2Atan%2836%29
h=49.16ft%2A0.38406
h=18.88ft -the height of the tree


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
dave is trying to measure the height of a pine tree in baguio. at a certain point on the same level ground as the base of the tree, he finds that the angle of elevation to the top of the tree is 48degree. Moving to a point 17ft farther, the angle of elevation becomes 36degree. find the height of the tree
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Draw the picture so you can SEE what you are doing.
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You have a right triangle.
The base is 17 ft
The height is the tree = h ft
The base angle where you are standing is 48 degrees
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Using trigonometry you get:
tan(48) = opp/adj = h/17
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h = 17*tan(48)
h = 17*1.11
height = 18.88 ft
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cheers,
Stan H.
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