1.

From a window 20m above the ground, a person could see the top of the house across the street at an angle of elevation of 5 degrees. The angle of depression to the base of the house was 15 degrees. What is the height of the house?

Answer»

ANSWER:

To find:  Height of the HOUSE

Tan 15 ° = 0.2679

Tan 5 ° = 0.0875

BC=AD

Step-by-step explanation:

In triangle ABC,                  

Tan 15 ° = AB/BC

0.2679 = 20/BC

BC = 20/0.2679

BC = 74.65 m

AC² =  AB²+ BC² ( Pythagoras THEOREM )

AC² = 20² + 74.65²

AC² = 400 + 5572.6

AC² = 5972.6

In triangle ADE,

Tan 5 ° = DE/AD

0.0875 = DE/BC    ( AD = BC )

BC * 0.0875 = DE

74.65 * 0.0875 = DE

DE = 6.53 m

DC² = AC² - AD²

DC² = 5972.6 - 5572.6

DC² = 400

DC = 20 m

So therefore the height of the house is ED + DC

ED + DC = 6.53 m + 20 m

EC = 26.53 m ( ED + DC = EC = HEIGHT OF THE HOUSE )

I hope you understood the answer


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