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Natalka [10]
3 years ago
13

The measure of one angle of a right triangle is 12 degrees more than the measure of the smallest angle. Find the measures of all

three angles.
Mathematics
1 answer:
Svet_ta [14]3 years ago
8 0

Answer:

90°, 51° and 39°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Let the smallest angle be x then the other angle is x + 12, thus

x + x + 12 + 90 = 180, that is

2x + 102 = 180 ( subtract 102 from both sides )

2x = 78 ( divide both sides by 2 )

x = 39

The other angle is 39 + 12 = 51

The 3 angles are 90°, 51° and 39°

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Answer:

<h2>The distance from the pitcher's mound and to second base is 37.99 approximately.</h2>

Step-by-step explanation:

The diamond is a square, which in this case has 50 feet long each side, and from home to pitcher is 38 feet. Notice that home is a vertex of the square and the pitcher's mound is the intersection of the diagonals, where they cut half.

We can find the distance from the pitcher to first base using Pythagorean's Theorem, where 50 feet is the hypothenuse.

50^{2} =38^{2}+x^{2}\\x^{2}=50^{2}-38^{2}\\x=\sqrt{2500-1444}\\ x=\sqrt{1056}\\ x \approx 32.5 \ ft

Therefore, the distance from the pitcher to first base is 32.5 feet, approximately.

Now, we can use again Pythagorean's Theorem to find the distance from pitcher to second base, where the hypothenuse is 50 feet.

50^{2}=32.5^{2}+y^{2}\\y^{2}=50^{2}-32.5^{2}\\y=\sqrt{2500-1056.25}\\ y =\sqrt{1443} \approx 37.99

Therefore, the distance from the pitcher's mound and to second base is 37.99 approximately.

<em>(this results make sense, because the diagonals of a square intersect at half, that means all bases have the same distance from pitcher's mound, so the second way to find the distance asked in the question is just using theory)</em>

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