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Answer:
The angle formed between the first base foul line and the path of the baseball is 63°.
Step-by-step explanation:
This is not a difficult problem. We only need to remember the measure of a right angle, which is 90°. Now, recall that the path baseball divides the right angle in two angles, and we know the measure of one of them.
In the attached figure the black lines are the foul lines of the baseball field, and the blue line is the baseball path. In green is the given angles and colored red is the wanted angle.
So, the sum of the angles α and β is 90° and we know the measure of the angle α: 27°. So,
α + β = 90° .
Then,
β = 90° - α = 90° - 27° = 63°.
Answer:
2√3
Step-by-step explanation:
You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).
The magnitude of R is 2√3.
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In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...
Sin = Opposite/Hypotenuse
sin(30°) = √3/R
R = √3/sin(30°) = √3/(1/2) = 2√3
Of course, doing this on your calculator will give a numerical answer, which you may not want.
