The sun is 25° above the horizon. Find the length of a shadow cast by a building that is 100 feet tall (see figure). (Round your answer to two decimal places.)
Draw a diagram.
Review your basic trig functions.
The shadow's length x is found by
x/100 = cot 25°
46.63
To find the length of the shadow cast by the building, we can use trigonometry. Specifically, we can use the tangent function.
The tangent of an angle can be calculated by taking the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle is the height of the building (100 feet) and the side adjacent to the angle is the length of the shadow.
So, we have the equation tan(25°) = (length of shadow) / 100.
To find the length of the shadow, we can rearrange the equation:
(length of shadow) = 100 * tan(25°).
Now, we can use a scientific calculator or an online tool to determine the value of tan(25°), which is approximately 0.466.
Plugging this value back into the equation, we get:
(length of shadow) = 100 * 0.466 = 46.6 feet.
Therefore, the length of the shadow cast by the building is approximately 46.6 feet.