Kathy is standing directly between two tall buildings which are 100 feet apart. Her eye level is 5 feet above the ground. Kathy looks up at the top of the taller building and the top of the shorter building with angles of 45 degrees and 38 degrees above the horizontal, respectively. What is the difference in height between the taller building and the shorter building, to the nearest foot?

Question

Lia

Mathematics

1 October, 04:46

Kathy is standing directly between two tall buildings which are 100 feet apart. Her eye level is 5 feet above the ground. Kathy looks up at the top of the taller building and the top of the shorter building with angles of 45 degrees and 38 degrees above the horizontal, respectively. What is the difference in height between the taller building and the shorter building, to the nearest foot?

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Brittany Schneider · Answer 1

Angle of taller building Tan 45° = opposite (height of the building) / adjacent 50 feet (distance between Kathy and the taller building

Tan 45° = 1

Height of taller building from eye level = multiplying adjacent 50 feet * Angle (Tan 45°) 1 = 50 feet opposite

Angle of smaller building Tan 38° = 0.781

Height of smaller building from eye level = Angle * adjacent 50 feet = 39.06 feet

Difference of eye level from ground is 5 feet

Taller building height is 50 + 5

Total height of taller building is 55 feet.

Smaller building height is 39.06 + 5

Total height of smaller building is 44.06 feet