A lifeguard is in an observation chair and spots a person who needs help. The angle of depression to the person is 22°. The eye level of the lifeguard is 10 feet above the ground. What is the horizontal distance between the lifeguard and the person? Round to the nearest foot.

The horizontal distance between the lifeguard and the person is approximately 24.751 feet.

Step-by-step explanation:

At first we include a geometrical representation of the statement, which is shown in the image attached below. We can determine the horizontal distance between the lifeguard and the person by means of the following trigonometrical relationship:

(1)

Where:

- Angle of depression to the person, measured in sexagesimal degrees.

- Height of the lifeguard above the ground, measured in feet.

- Horizontal distance between the lifeguard and the person, measured in feet.

If we know that and , then the horizontal distance between the lifeguard and the person is:

The horizontal distance between the lifeguard and the person is approximately 24.751 feet.

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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