SOLUTION: Jane and mark each build ramps to jump their remote-controlled cars. Both ramps are right triangles when viewed from the side, The incline of Jane's ramp makes a 30-degree angle wi

Question 1089747: Jane and mark each build ramps to jump their remote-controlled cars. Both ramps are right triangles when viewed from the side, The incline of Jane's ramp makes a 30-degree angle with the ground, and the length of the inclined ramp is 16 inches. The incline of Mark's ramp makes a 45-degree angle with the ground, and the length of the inclined ramp is 12 inches.
Part A: What is the horizontal length of the base of each ramp? Explain how you found you answers.
Part B: Which car is launched from the highest point? Explain your reasoning.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
in a right triangle the cosine is defined as the adjacent side divided by the hypotenuse
:
in a right triangle the sine is defined as the opposite side divided by the hypotenuse
:
Part A
:
cos(30) = x / 16
x = cos(30) * 16 = 13.86 inches
:
cos(45) = y / 12
y = cos(45) * 12 = 8.49 inches
:
Jane's ramp has a horizontal distance of 13.86 inches
Mark's ramp has a horizontal distance of 8.49 inches
:
Part B
:
sin(30) = x / 16
x = sin(30) * 16 = 8 inches
:
sin(45) = y / 12
y = sin(45) * 12 = 8.49 inches
:
Mark's car is launches from the highest point(8.49 inches)
:

RELATED QUESTIONS
Antonio and Angelo are racing with remote-controlled cars around a track. Antonio's... (answered by lwsshak3)

A recommendation for wheelchair ramps is that the rise-to-run ratio be no greater than... (answered by ikleyn)

My son is having a difficult time with this slope problem, and I just don't remember... (answered by LolaFish)

Please help me find the length of the base and diagonal for 2 handicap ramps with known... (answered by ccs2011,Theo,stanbon)

Jack and Mark live 4 miles apart from each other on Baseline Road. At 6 pm, their moms... (answered by jorel1380)

Tom and Jeri are playing with two remote control cars on a straight track. Tom's car... (answered by ankor@dixie-net.com)

You are sliding a big cabinet down a truck ramp for a customer. You must maintain control (answered by jim_thompson5910)

I need help solving this problem.You are sliding a big cabinet down a truck ramp for a... (answered by ankor@dixie-net.com)

You want to make a ramp to your front door instead of steps. The commercial code for a... (answered by stanbon)