ANGLE OF ELEVATION, The height of an outdoor basketball backboard is 12 1/2 feet and the backboard casts a shadow 17 1/8 feet long.
36.12 deg
To find the angle of elevation, we can use the tangent function, which relates the angle of elevation to the height and the shadow length.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.
In this scenario, we have a right triangle where the height of the basketball backboard (opposite side) is 12 1/2 feet and the shadow length (adjacent side) is 17 1/8 feet.
First, let's convert the measurements to a common format. Converting 1/2 to an eighth, the height becomes 12 4/8 feet, and converting 1/8 to fifths, the shadow length becomes 17 5/8 feet.
Now, we can calculate the tangent of the angle of elevation:
Tangent(angle) = Opposite / Adjacent
Tangent(angle) = 12 4/8 / 17 5/8
To perform the calculation, we need to convert the mixed numbers to improper fractions:
Tangent(angle) = 20/2 / 28/8
Tangent(angle) = (20/2) * (8/28)
Tangent(angle) = 160/56
Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor (8), we get:
Tangent(angle) = 20/7
Now, we can find the angle of elevation by taking the inverse tangent (also known as arctangent) of 20/7:
Angle = Inverse Tangent(20/7)
Angle = arctan(20/7)
Using a calculator or an online tool, we find that the angle of elevation is approximately 71.57 degrees.
Therefore, the angle of elevation for the basketball backboard is approximately 71.57 degrees.