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Fofino [41]
1 year ago
6

Find the length of the leg a of a right triangle with leg length b = 21.5 inches and the hypotenuse c = 31.9 inches. Use a calcu

lator to estimate the square root to one decimal place.The length of the leg is approximately _____inches.
Mathematics
1 answer:
mylen [45]1 year ago
4 0

The length of the leg a of the right triangle is obtained by applying the Pythagorean theorem which is given as:

\text{opposite}^2+adjacent^2=hypothenus^2

Thus, we have that:

a^2+b^2=c^2

Given that b = 21.5 inches and c = 31.9 inches, we now have:

a^2+(21.5)^2=(31.9^2)a^2+462.25=1017.61a^2=1017.61-462.25a^2=555.36\begin{gathered} a=\sqrt[]{555.36}=23.57 \\ \Rightarrow a=23.6\text{ inches (to one decimal place)} \end{gathered}

Therefore, the length of the leg a of the right triangle is 23.6 inches

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