Question

Claire and Marisa are both waiting to get a rebound during a basketball game. If the height of the basketball hoop is 10 feet, the angle of elevation between Claire and the goal is 35°, and the angle of elevation between Marisa and the goal is 25°, how far apart are they standing?

Answer 1

1. Let's represent the distance between Marisa and Claire with the letter "x".

 2. You must find the distance between them and the goal (Adjacent leg).

 3. The distance between Marisa and the goal (dA) is:

 Tan(α)=Opposite leg/Adjacent leg

 α=25°
 Opposite leg=10 feet
 Adjacent leg=dA

 Tan(25°)=10/dA

 4. Let's clear dA:

 dA(Tan(25°))=10
 dA=10/Tan(25°)
 dA=21.44 feet

 5. The distance between Claire and the goal (dB) is:

 Tan(β)=Opposite leg/Adjacent leg

 β=35°
 Opposite leg=10 feet
 Adjacent leg=dB

 Tan(35°)=10/dB
 dB(Tan(35°))=10
 dB=10/Tan(35°)
 dB=14.28 feet

 6. Therefore, the distance between Marisa and Claire is:

 x=dA-dB
 x=21.44 feet-14.28 feet
 x=7.16 feet

 How far apart are they standing?

 The answer is: 7.16 feet