SOLUTION: From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. From a point B that is 46 feet further from the tree, the angle of elevation is 22 degre

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Question 1197859: From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. From a point B that is 46 feet further from the tree, the angle of elevation is 22 degrees. Which of the following is the height of the tree.
A. 34.1 feet
B. 35.8 feet
C. 36.7 feet
D. 37.2 feet
E. 38.5 feet
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Try to draw a figure of the description.

x, distance from A to bottom of tree
46, length AB
y, how tall the tree



You can substitute for x, and simplify and solve for y.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
From a point A on level ground, the angle of elevation to the top of a tree is 38 degrees. From a point B that is 46 feet further from the tree, the angle of elevation is 22 degrees. Which of the following is the height of the tree.
A. 34.1 feet
B. 35.8 feet
C. 36.7 feet
D. 37.2 feet
E. 38.5 feet
.
As ∡CAD = 38o, ∡CAB = 180 - 38 = 142o
In ΔABC, ∡BCA = 180 - (142 + 22), or 38 - 22 = 16o
Use Law of Sines to find AC, as follows:  
                                      AC * sin 16o = 46 * sin 22o ------ Cross-multiplying
                                               
                                               Continue solving for AC

                                 We then have: 
                                              
Since AC is already known (from above), you need to CONTINUE onward and solve for CD, the height of the tree. 

When done, you should get a height of approximately 38.49115544, which when rounded to 1 decimal place, is about 38.5'(CHOICE E.).
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