Final answer:
To calculate the length of the shadow cast by a 92 ft tall building when the Sun is 58 degrees above the horizon, use the formula L = height / tan(angle). After finding the tangent of 58 degrees and computing L, the answer is rounded to the nearest tenth.
Step-by-step explanation:
To find the length of the shadow cast by a 92 ft tall building when the Sun is 58 degrees above the horizon, we need to use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation of the sun, the height of the object, and the length of the shadow that the object casts. The formula for the tangent of an angle in a right triangle is the opposite side (the height of the building) divided by the adjacent side (the length of the shadow).
Let the shadow's length be L, the building's height 92 ft, and the angle of elevation of the Sun 58 degrees. The relation is given by:
tan(58°) = height / L
L = height / tan(58°)
Using this formula:
L = 92 ft / tan(58°)
The exact value will depend on the tangent of 58 degrees. After calculating the tangent of 58 degrees and dividing the building's height by this value, we round the resulting length of the shadow to the nearest tenth.