Dereck and Sam are standing 3.1 feet apart.
The situation forms two right angle triangle.
A right angle triangle is a triangle that has one of its angles as 90 degrees.
Derek looks at a 10 foot basketball goal with an angle of elevation of 29°.
Sam looks at the goal with an angle of elevation of 43°.
Sam is directly in front of Dereck. Therefore,
Dereck distance from the base of the basket ball can be found as follows:
tan 29 = opposite / adjacent
opposite side = 10 ft - 5.83 ft = 4.17 ft
tan 29 = 4.17 / x
x = 4.17 / 0.55430905145
x = 7.52287913948
x = 7.523
Sam distance from the base of the basket ball can be found as follows
tan 43 = 4.17 / y
y = 4.17 / 0.93251508613
y = 4.47177752084
y = 4.471
There feet apart = 7.523 - 4.471 = 3.052 = 3.1 feet
learn more on elevation here:https://brainly.com/question/24442138?referrer=searchResults
