the angle of elevation of the sun is 27 degree.a man is 180cm tall.how long is his shadow?give your answer to the nearest 10cm.
To determine the length of the man's shadow, we can use trigonometry. Specifically, we can make use of the tangent function.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, the man's height of 180cm represents the length of the opposite side, while the length of his shadow represents the length of the adjacent side. The angle of elevation of the sun, 27 degrees, is the angle between the ground and the line from the top of the man's head to the tip of his shadow.
Using the tangent function, we can write the equation as follows:
tan(27°) = opposite / adjacent
Solving for the adjacent side (length of the shadow), we have:
adjacent = opposite / tan(27°)
Plugging in the known values:
adjacent = 180cm / tan(27°)
Using a calculator:
adjacent ≈ 225.84cm
Rounding to the nearest 10cm, the length of the man's shadow is approximately 230cm.