Question 1044038
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
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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.