Dr. Black is standing 20 feet from a streetlamp. The lamp is making his shadow 5 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 30. To the nearest foot, the streetlamp is about _____.

Dr. Black was standing 20 feet from his streetlamp outside his home. The lamp made Dr. Black's shadow approximately 5 feet long. His estimate was that angle of elevation from the tip of his shadow to the streetlamp is approximately 30. To the nearest foot, the streetlight outside his home is 14ft.

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MsEHolt MsEHolt · Answer 2 · 2018-08-01T02:51:58+02:00

The correct answer is:

14 ft.

Explanation:

Let x be the height of the street lamp. This is one leg of a right triangle.

The other leg is formed by the combination of the length of the shadow and the distance Dr. Black is standing from the lamp. This is 5+20 = 25.

The angle of elevation is 30°. Comparing the given sides to this angle, we have the side opposite the angle (x) and the side adjacent to the angle (25). We know that opposite/adjacent is the ratio for tangent; this gives us the equation:

[tex] \tan 30=\frac{x}{25}
\\
\\\text{Multiplying both sides by 25 gives us:}
\\
\\25 \times \tan 30 = (\frac{x}{25})\times 25
\\25 \times \tan 30 = x
\\14.43 = x
\\14\approx x [/tex]