The height of an outdoor basketball backboard is 12 1/3 feet and the backboard casts a shadow 19 1/5 feet. Find the angle of elevation of the sun (answer in units of degrees). Can someone help me with the formula? Thank you!

If the angle is x,

tan x = 12.3333/19.2

Better review your trig ratios...

To find the angle of elevation of the sun, we can use the trigonometric function called tangent (tan).

Step 1: Identify the sides of the right-angled triangle formed by the basketball backboard and its shadow.

Let the height of the backboard be 'a' and the length of its shadow be 'b'.

In this case, the height of the backboard (a) is given as 12 1/3 feet, which can be written as a mixed number 12 + 1/3 = 37/3 feet.

The length of the shadow (b) is given as 19 1/5 feet, which can be written as a mixed number 19 + 1/5 = 96/5 feet.

Step 2: Determine the trigonometric function to use.

Since we have the known length of the opposite side (a) and the adjacent side (b), we can use the tangent function.

Step 3: Apply the tangent function to find the angle of elevation.

The tangent (tan) of an angle is calculated as the ratio of the length of the opposite side to the adjacent side in a right-angled triangle.

tan(angle) = opposite/adjacent

In this case, tan(angle) = (37/3) / (96/5)

Step 4: Calculate the angle of elevation using the inverse tangent (arctan) function.

The arctan function is the inverse of the tangent function, and it helps us find the angle when we know the ratio. In mathematical notation, arctan(tan(angle)) = angle.

So, the angle of elevation (in degrees) can be found by evaluating:

angle = arctan((37/3) / (96/5))

This will give you the value of the angle of elevation of the sun.