SOLUTION: From the stage of a theater, the angle of elevation to the first balcony is 19 degrees. The angle of elevation to the second balcony, 6.3 meters directly above the first, is 29 deg

Question 1044038: From the stage of a theater, the angle of elevation to the first balcony is 19 degrees. The angle of elevation to the second balcony, 6.3 meters directly above the first, is 29 degrees. How high above stage level is the first balcony, to the nearest tenth of a meter?
a. 8.5 meters
b. 10.3 meters
c. 12.4 meters
d. 14.2 meters
e. 16 meters
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Call the horizontal distance to the first balcony (a leg of the triangle) x.
Then the height of the balcony from that spot is h.
tangent of y=h/x
x=h/tan 19
-------------------
To the second balcony, it will be x=(h+6.3)/tan 29
Set the two equal to each other since they are both equal to x.
h/tan 19=(h+6.3/tan 29
cross-multiply
h tan 29=(h+6.3) tan 19=h tan 19+6.3 tan 19
h tan 29-h tan 19=6.3 tan 19=2.17
h(tan 29-tan 19)=2.17
0.21 h=2.17 i
h=10.3 m ANSWER IS A
Check using 10.33, the answer to two decimal places
x, the horizontal distance, is 30 m.
10.33/30=0.3433, and tan ^(-1) of that is 19.00 degrees
16.33/30=0.5543 and tan ^(-1) of that is 29.00 degrees.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let the horizontal distance from the balconies be
if the height to the 1st balcony is , than the height to the 2nd balcony is
if the angle of elevation to the first balcony is degrees, you use right angle triangle whose legs are and , and we will have

=>
the second balcony, 6.3 meters directly above the first, is 29 degrees, so we have

=>
since same in both cases, we have:

...........cross multiply

...round it

so, your answer is: b. meters

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