Question

A right triangle has a leg of 5 inches and a hypotenuse of 7 inches. What is the length of the other leg?

Enter your answer, as a decimal rounded to the nearest tenth, in the box.

Answer 1

a² + b² = c²

a² = 7² - 5²

a² = 24

a = √24

a = 4.9 inches (nearest tenth)

Answer: 4.9 inches

Answer 2

`(Base)=√(24) {\text{inches}`

Explanation:

It is given that A right triangle has a leg of 5 inches and a hypotenuse of 7 inches, thus using the trigonometry, we have

`(Hyp)^2=(Base)^2+(Per)^2`

Substituting the given values, we have

`(7)^2=(Base)^2+(5)^2`

⇒
`49=(Base)^2+25`

⇒
`49-25=(Base)^2`

⇒
`24=(Base)^2`

⇒
`(Base)=√(24) {\text{inches}`

Thus, the length of the other leg is
`√(24) {\text{inches}`.