Question

Both Derek and Sam are 5 feet 10 inches tall. Derek looks at a 10 foot basketball

Answer 1

Dereck and Sam are standing 3.1 feet apart.

The situation forms two right angle triangle.

What is a 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

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