Question

Help!! Please!!

Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.

Answer 1

Explanation:

x=10+4=14

14+14=28

the answer is 28 fts

Answer 2

The answer is 6.67 feet, approximately.

Explanation:

The image attached shows the context that the problems refered.

Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.

`\angle AOB \cong \angle COD`

`\angle AOB= \angle COD=90\° - a`

Remember that the tangent function is defined as

`tan(\theta)=(Opposite \ Leg)/(Adjacent \ Leg)`

Replacing each equiavlence, we have

`tan(90-a)=(6)/(4)=(10)/(x)`

Then, we solve for
`x`

`(6)/(4) =(10)/(x)\\ x=(40)/(6)\\ x \approx 6.67 ft`

Thereofre, the answer is 6.67 feet, approximately.