Question

Maddie throws a baseball from third base to first base. The four 90-foot lines between the bases form a square. Which number is the best estimate of how far Maddie throws the baseball?

What is the height of the ramp, to the nearest foot?
Question 4 options
90 feet
130 feet
150 feet
180 feet

A cyclist pedals up a hill that has a 13° angle. If the cyclist pedals up the hill for 10 kilometers, what is the change in her elevation, x ?

0.22 kilometer


9.7 kilometers


2.2 kilometers


45.0 kilometers

Answer 1

It seems like there are only two problems here. Problem 1 is the one with Maddie throwing the baseball. Problem 2 deals with the cyclist. For some reason you threw in "What is the height of the ramp, to the nearest foot?" in the middle of the baseball problem. That seems like a typo?

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Problem 1 (baseball problem with Maddie)

a = 90
b = 90
c = unknown

Pythagorean Theorem
a^2+b^2 = c^2
90^2+90^2 = c^2
8100+8100 = c^2
16200 = c^2
c^2 = 16200
sqrt(c^2) = sqrt(16200)
c = 127.279220613579

If we round to the nearest ten, then we get 130. In other words, 127.279 is closer to 130 than it is to 120.

So it looks like "130 feet" (choice B) is the final answer.
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Problem 2 (cyclist on a hill problem)

sin(angle) = opposite/hypotenuse
sin(13) = x/10
10*sin(13) = 10*x/10
10*sin(13) = x
x = 10*sin(13)
x = 2.24951054343864
x = 2.2

Answer: 2.2 km