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You are on the roof of a building and see a friend standing 190 meters away from the base of a building. The angle of depression to your friend is
28^(@). How far below are they?
They are
◻ meters below you (round your answer to three decimal places)

You are on the roof of a building and see a friend standing $190$ meters away from the base of a building. The angle of depression to your friend is $28^{\circ}$ . How far below are they? $\newline$ They are $\square$ meters below you (round your answer to three decimal places)

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Pythagorean theorem

Full solution

Q. You are on the roof of a building and see a friend standing

190

meters away from the base of a building. The angle of depression to your friend is

28^{\circ}

. How far below are they?

\newline

They are

\square

meters below you (round your answer to three decimal places)

Identify Relationship: Identify the relationship between the angle of depression and the angle of elevation. $\newline$ The angle of depression from the roof to the friend is equal to the angle of elevation from the friend to the point on the roof directly above the observer due to alternate interior angles being equal when two lines are parallel.
Triangle Type: Determine the triangle type and the sides involved. $\newline$ The situation forms a right-angled triangle with the building as the height $h$ , the distance from the friend to the building as the adjacent side ( $190$ meters), and the angle of elevation ( $28$ degrees) at the friend's position.
Trigonometry Calculation: Use trigonometry to find the height below. $\newline$ The tangent of the angle of elevation is equal to the opposite side (height of the building, $h$ ) divided by the adjacent side (distance from the friend to the building). $\newline$ $\tan(28^\circ) = \frac{h}{190}$
Solve for Height: Solve for $h$ (the height below). $h = 190 \times \tan(28^\circ)$ Calculate the value using a calculator. $h \approx 190 \times 0.531709$ $h \approx 101.02471$
Round Answer: Round the answer to three decimal places. $h \approx 101.025$ meters

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