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RUDIKE [14]
3 years ago
12

The tower is 650 meters high. Suppose a building is erected such that the base of the building is on the same plane as the base

of the​ tower, the angle of elevation from the top of the building to the top of the tower is 80.38° and the angle of depression from the top of the building to the foot of the tower is 65.05​°. How high would the building have to​ be?
Mathematics
1 answer:
madam [21]3 years ago
3 0

Answer:

173.57\ m

Step-by-step explanation:

Let

h -----> the height of the building

x -----> the horizontal distance between the building and the tower

we know that

tan(80.38\°)=(650-h)/x

solve for x

x=(650-h)/tan(80.38\°) -----> equation A

tan(65.05\°)=h/x

solve for x

x=h/tan(65.05\°) ------> equation B

equate equation A and equation B and solve for h

h/tan(65.05\°)=(650-h)/tan(80.38\°)

tan(80.38\°)h=(650-h)tan(65.05\°)

tan(80.38\°)h=(650)tan(65.05\°)-(h)tan(65.05\°)

h[tan(80.38\°)+tan(65.05\°)]=(650)tan(65.05\°)

h=(650)tan(65.05\°)/[tan(80.38\°)+tan(65.05\°)]  

h=173.57\ m

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