the angle of elevation of the sun is 27 degree.a man is 180cm tall.how long is his shadows?give your answer to the nearest 10cm
180/x = tan 27°
To find the length of the man's shadow, you can use the tangent function. The tangent of the angle of elevation is equal to the opposite side divided by the adjacent side in a right triangle. In this case, the man's height is the opposite side, and the length of his shadow is the adjacent side.
Let's suppose the length of his shadow is "x" cm.
Using the tangent function, we have:
tan(27°) = Opposite/Adjacent
tan(27°) = 180/x
Rearranging the equation, we can solve for x:
x = 180 / tan(27°)
Calculating this value, we get:
x ≈ 376 cm
Therefore, the man's shadow is approximately 376 cm long when rounded to the nearest 10 cm.
To find the length of the man's shadow, we can use trigonometry. Let's call the length of the shadow "x".
First, let's draw a diagram to visualize the situation. Draw a straight line vertically to represent the man's height of 180cm. Then, draw another line from the top of the man's head to represent the sun's rays at an angle of elevation of 27 degrees. This line will intersect with the ground, forming a right triangle.
The angle of elevation is measured between the ground and the sun's rays. As the angle of elevation and the angle of depression (measured from the sun to the man's head) are equal, we can use the angle of depression to solve the problem.
In a right triangle, we can use the tangent function (tan) to relate the angle of depression to the opposite side (his shadow length) over the adjacent side (his height). The formula is:
tan(angle) = opposite / adjacent
In this case, the angle is 27 degrees, the opposite side is x (the length of the shadow), and the adjacent side is the height of the man, which is 180cm.
So, we have:
tan(27°) = x / 180
To solve for x, we can multiply both sides of the equation by 180:
x = tan(27°) * 180
Using a calculator, evaluate tan(27°) to be approximately 0.5095. Plugging this value into the equation, we get:
x = 0.5095 * 180
x ≈ 91.71
Rounding to the nearest 10cm, the length of the man's shadow is approximately 90cm.