A roof has an agle of 32 degrees. If the lenght of the base of the roof is 48 ft, how tall is the roof?
To find the height of the roof, we can use basic trigonometry. In this case, we have the angle of the roof and the length of the base, so we can use the tangent function.
Tangent (tan) is defined as the ratio of the opposite side to the adjacent side of a right triangle.
In this case, the opposite side is the height of the roof, and the adjacent side is the length of the base.
Using the formula for tangent:
tan(angle) = height/base
Rearranging the formula:
height = base * tan(angle)
Now we can substitute the values given:
height = 48 ft * tan(32 degrees)
To calculate the value of tan(32 degrees), you can use a scientific calculator or an online calculator that has trigonometric functions.
Using a calculator, we find that tan(32 degrees) is approximately 0.6249.
So, substituting this value back into the equation:
height = 48 ft * 0.6249
Calculating this:
height = 29.9968 ft
Therefore, the height of the roof is approximately 30 ft.