Question

Find the length of the hypotenuse of a right triangle with legs of 15 inches and 7 inches.

Answer 1

16.55

Explanation:

`√(7) ^ {2} +15^(2)`

Answer 2

`\boxed {\boxed {\sf \sqrt {274} \ or \ 16.55 \ inches}}`

Explanation:

The sides of a right triangle can be found using Pythagorean Theorem.

`a^2+b^2=c^2`

where a and b are legs and c is the hypotenuse.

In this triangle, the legs are 15 and 7, so we can substitute those values in for a and b.

`(15)^2+(7)^2=c^2`

Solve the exponents.

• 15²=15*15=225
• 7²=7*7=49

`225+49=c^2`

Add.

`274=c^2`

Since we are solving c, we have to isolate the variable. It is being squared and the inverse of a square is a square root. Take the square root of both sides.

`\sqrt {274}=\sqrt {c^2}`

`\sqrt {274}=c \\ $$16.5529453572= c`

Let's round to the nearest hundredth. The 2 in the thousandth place tells us to leave the 5.

`16.55 \approx c`

The hypotenuse is approximately √274 or 16.55 inches