Avani is trying to find the height of a radio antenna on the roof of a local building. She
stands at a horizontal distance of 21 meters
from the building. The angle of elevation
from her eyes to the roof (point A) is 42°,
and the angle of elevation from her eyes to
the top of the antenna (point B) is 51°. If
her eyes are 1.5 meters from the ground,
find the height of the antenna (the distance
from point A to point B). Round your
answer to the nearest meter if necessary.

The height of the antenna is 7.0 m

Step-by-step explanation:

Let the height of the antenna be represented by x, and the distance from Avani's eyes to the top of the building A by y. And let z = x + y, so that:

Tan 42 =

y = Tan 42 x 21

  = 0.9004 x 21

  = 18.9084

y = 18.91 m

Also,

Tan 51 =

z = Tan 51 x 21

  = 1.2349 x 21

  = 25.9329

z = 25.93 m

Therefore,

x = z - y

  = 25.93 - 18.91

  = 7.02

x = 7.02 m

The height of the antenna is 7.0 m

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step-by-step explanation: