The angle of elevation of the sun is 31 degrees. Find the length of the shadow, to the nearest foot, of a man that is 6 feet tall.

length of shadow --- x ft

tan31° = 6/x
x = 6/tan31 = 9.98567... or appr 10 ft

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Wank

To find the length of the shadow, we can use the concept of trigonometry. The angle of elevation of the sun is the angle between the horizontal line and the line from the top of the man's head to the top of the shadow.

So, in this case, we can consider the man's height as the length of the side opposite to the angle of elevation and the length of the shadow as the length of the side adjacent to the angle of elevation.

We can use the tangent function (tan) to find the length of the shadow. The tangent of an angle is the ratio of the length of the side opposite to the length of the side adjacent.

In this case, the tangent of the angle of elevation is equal to the height of the man divided by the length of the shadow.

Using this information, we can set up the trigonometric equation:

tan(31 degrees) = height / length of shadow

Substituting the known values:

tan(31 degrees) = 6 / length of shadow

Now, we can solve for the length of the shadow:

length of shadow = 6 / tan(31 degrees)

Using a calculator, we determine:

length of shadow ≈ 10.76 feet

Therefore, the length of the shadow, to the nearest foot, is approximately 11 feet.