SOLUTION: A 45 - 45 - 90 triangle has a hypotenuse of length 15 units. What is the length of one of the legs? If necessary, round your answer to two decimal places.

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Question 214697: A 45 - 45 - 90 triangle has a hypotenuse of length 15 units. What is the length of one of the legs? If necessary, round your answer to two decimal places.
Found 2 solutions by rfer, drj:
Answer by rfer(3384) About Me  (Show Source):
You can put this solution on YOUR website!
Since the angles are equal, the legs will be equal.
15^2=a^2+b^2
225=112.5+112.5
sq rt of 112.5=10.6

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A 45 - 45 - 90 triangle has a hypotenuse of length 15 units. What is the length of one of the legs? If necessary, round your answer to two decimal places.

Step 1. Let c=15 be the hypotenuse.

Step 2. Since the complementary angles are equal, their opposite sides are equal. Let s be the side of the legs.

Step 3. Using the Pythagorean Theorem given as the square of the legs (given as a and b) equal to square of the hypotenuse or c%5E2=a%5E2%2Bb%5E2. For this example, a=b=s.

Step 4. Then

c%5E2=s%5E2%2Bs%5E2

c=2s%5E2

c%2F2=s%5E2

sqrt%28c%2F2%29=sqrt%28s%5E2%29

sqrt%2815%2F2%29=s

s=sqrt%2815%2F2%29=2.739=2.74

Step 5. ANSWER: The length of the both legs is 2.74 units.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J