Question 1041217: To measure the height of a tree, Steve measures the angle of elevation of the treetop as 47 degrees .47°. He then moves 20 ft20 ft closer to the tree and from this new point measures the angle of elevation to be 58 degrees .58°. How tall is the tree?
Found 4 solutions by josgarithmetic, Boreal, addingup, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Large right triangle, y height, x bottom leg, 47 degree at end of that leg.
Small right triangle, y height, x-20 bottom leg, 58 degree at end of this leg.
The only unknown variables are x and y. Use tangent function values. Height y is how tall the tree.
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! I'm going to ignore the second number. Drawing this helps.
angle of elevation is 47 degrees, moves 20 feet closer and angle of elevation is 58 degrees.
The height of the tree doesn't change.
tangent of 47=height/distance, which I will call x. So tan 47=h/x;
tan 57=h/(x-20)
1.0724x=h
1.5399(x-20)=h; 1.5399x-30.798=h
Set these two equal, since they both equal h.
1.0724x=1.5399x-30.798
subtract 1.5399x from both sides
-.4675x=-30.798
x=65.88 feet. But that isn't h.
1.0724 (65.88)=h=70.65 feet ANSWER
From 65.88 feet, the elevation is 47 degrees
from 45.88 feet, the elevation is 57 degrees for a tree 70.65 feet tall.
Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! IF you look at my drawing you can see (in blue) the lines describing what the problem says. Then I drew in yellow a fact that is very important in solving this problem: You have two right angle triangles.
:
We will use the tan function:
Equation 1:
height
------- = tan(47)
20+z
:
Equation 2:
height
------ = tan(58)=
z
:
height
------ = z Use this value for z in the first equation:
tan(58)
:
height
---------- = tan(47)
(20+height)/tan(58)
:
height
= ------------- = 1.07
(20+height)/1.6
:
21.4+1.07(height)/1.6 = height
21.4 = 0.669(height) = height
height = 21.4/0.669 = 32 ft
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
To measure the height of a tree, Steve measures the angle of elevation of the treetop as 47 degrees .47°. He then moves 20 ft20 ft closer to the tree and from this new point measures the angle of elevation to be 58 degrees .58°. How tall is the tree?
Use TRIG ratios, or law of sines to get the tree's height of: 
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