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One of the legs of a right triangle measures
15cm and its hypotenuse measures
17cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm

One of the legs of a right triangle measures $15 \mathrm{~cm}$ and its hypotenuse measures $17 \mathrm{~cm}$ . Find the measure of the other leg. If necessary, round to the nearest tenth. $\newline$ Answer: $\square$ $\mathrm{cm}$

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Circles: word problems

Full solution

Q. One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

Answer:

\square

\mathrm{cm}

Apply Pythagorean Theorem: To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse $c$ is equal to the sum of the squares of the lengths of the other two sides $a$ and $b$ . The formula is $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse and $a$ and $b$ are the legs of the triangle.
Given Values: We are given that one of the legs $a$ is $15$ cm and the hypotenuse $c$ is $17$ cm. We need to find the length of the other leg $b$ . We can rearrange the Pythagorean theorem to solve for $b$ : $b^2 = c^2 - a^2$ .
Substitute Values: Substitute the given values into the equation: $b^2 = 17^2 - 15^2$ . This simplifies to $b^2 = 289 - 225$ .
Calculate Difference: Calculate the difference: $b^2 = 289 - 225 = 64$ .
Find Square Root: Find the square root of $b^2$ to get the value of $b$ : $b = \sqrt{64} = 8\,\text{cm}$ .

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