Question

standard 14 homework
score: 4/30 answered: 3/18
progr
question 4
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suppose ( b = 5 ) in the right triangle shown above. find exact values for the lengths of the other sides; no
decimals allowed.
( a=)
( c=)
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Explanation:

Step1: Determine the relationship between sides \(a\) and \(b\)

In a \(45 - 45-90\) right - triangle, the legs are equal. So \(a = b\).
Since \(b = 5\), then \(a=5\).

Step2: Use the Pythagorean theorem to find \(c\)

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 5\) and \(b = 5\) into the formula: \(c^{2}=5^{2}+5^{2}=25 + 25=50\).
Take the square root of both sides: \(c=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\).

Answer:

\(a = 5\)
\(c = 5\sqrt{2}\)