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DochEvi [55]
3 years ago
9

Timelimit: 15 minutes. 11:08 remaining, x A radio tower is located 250 feet from a building. From a window in the building, a pe

rson determines that the angle of elevation to the top of the tower is 38 and that the angle of depression to the bottom of the tower is 27. How tall is the tower? Preview feet Points possible: 1 This is attempt 1 of 1. Submit

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
8 0

Answer:

The height of tower is 322.7 feet.

Step-by-step explanation:

Given

Distance between a building and tower= 250 feet

BCDE is a rectangle .Therefore, we have  BC=ED and CD=BE=250 feet

In triangle ABE

tan\theta=\frac{perpendicula \; side }{hypotenuse}

\theta=38^{\circ}

tan38^{\circ}=\frac{AB}{BE}

\frac{AB}{250}=0.781

AB=0.781\times250

AB=195.25 feet

In triangle EDC

\theta=27^{\circ}

tan27^{\circ}=\frac{ED}{CD}

\frac{ED}{250}=0.509

ED=250\times0.509

ED=127.25 feet

ED=BC=127.25 feet

The height of tower=AB+BC

The height of tower=195.25+127.25=322.5 feet

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