Anghelouid
Answered

A tower 135 ft high stands on the water's edge of a lake. From the top of the tower, the angle of depression of an object on the water's edge on the other side of the lake is 36.3 degree. What is the distance across the lake?

Sagot :

the distance is 99.167 or 99.17
Angle of Depression:  
1) Find the complementary angle of 36.3°:
    90° - 36.3° = 53.7°

2) Find the distance (x) across the the lake (base), given the height (side) of 135 feet opposite the complementary angle of 53.7°:

    Tangent = opposite
                    adjacent
    Tan (53.7°) = 135 feet
                            x
     
     1.3613(x) = 135 feet.
     1.3613x = 135 feet
     1.3613      1.3613
     
       x = 99.1699 or 99.17 feet is the distance across the lake.




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