A radio antenna

Avanti 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 1.54 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.

Correct answer:

h =  7 m

Step-by-step explanation:

x=21 m α=42  β=51  h1=1.54 m  tan α  = y1:x y1=x tanα=x tan42° =21 tan42° =21 0.900404=18.90848 m H1=y1+h1=18.9085+1.5420.4485 m  tan β  = y2:x y2=x tanβ=x tan51° =21 tan51° =21 1.234897=25.93284 m  h=y2y1=25.932818.9085=7 m

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