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5. A spotlight is mounted 7.3 meters high on a pole to illuminate the center of a parking area at

point A. If A is 10.2 meters from the base of the pole,at what angle of depression, 0, should

the spotlight be aimed?

User Emetiel
by
4.1k points

1 Answer

6 votes

Answer: 54.4°

Explanation:

If the spotlight is mounted 7.3 meters high, its height will be 7.3meters.

If A is 10.2 meters from the base of the pole, the base of the pole to the parking area will be 10.2meters

The angle of the depression will be facing the base directly therefore, the base will be the opposite of the triangle formed and the height of 7.3m will be the adjacent.

To get the depression angle, we use the trigonometry identity SOH, CAH, TOA

Since we have opposite and adjacent, we will use "TOA" which means

Tan theta = Opposite/Adjacent

Opposite = 10.2m Adjacent = 7.3

Tan theta = 10.2/7.3

Tan theta = 1.39

theta = arctan 1.39

Theta = 54.4°

The angle of depression that the spotlight should aim at is 54.4°

User ESPiYa
by
4.2k points