Prove that the absolute value of the sum is less than the sum of the absolute values
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Answer:
<em>The building is 61.5 m tall</em>
Step-by-step explanation:
The image below is a diagram where all the given distances and angles are shown. We have additionally added some variables:
h = height of the building
a, b = internal angles of each triangle
x = base of each triangle
The angles a and b can be easily found by subtracting the given angles from 90° since they are complementary angles, thus:
a = 90° - 37° = 53°
b = 90° - 42° = 48°
Now we apply the tangent ratio on both triangles separately:
From the last equation:
Substituting into the first equation:
Operating on the right side:
Rearranging:
Solving for h:
Calculating:
h = 61.5 m
The building is 61.5 m tall
