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Annette [7]
3 years ago
10

Determine the length of the leg of a 45o – 45o – 90o triangle with a hypotenuse length of 15 inches. ( ANSWER NEEDS TO BE IN RED

UCED RADICAL FORM )
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
3 0

Answer:

The lenghts of both legs: \frac{15\sqrt{2}}{2}\ inches

Step-by-step explanation:

By definition, when a triangle has angles that measures 45°, 45° and 90°, its legs are congruent.

Then, knowing the lenght of the hypotenuse, we can find the lenght (in inches) of  any leg of the given triangle by applying the Trigonometric Identity sin\alpha=\frac{opposite}{hypotenuse}:

sin(45\°)=\frac{leg}{15}\\\\leg=\frac{15}{\sqrt{2}}

Finally, simplifying, we get:

leg=\frac{15(\sqrt{2})}{(\sqrt{2})(\sqrt{2})}=\frac{15\sqrt{2}}{2}

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