Question

What is the length of the unknown leg in the right triangle?

A right triangle has a side with length StartRoot 23 EndRoot yards and hypotenuse with length StartRoot 87 EndRoot yards

Answer 1

a. 8 yd

Explanation:

Hypotenuse =
`√(87)`

Length =
`√(23)`

x² + (
`√(23)`)² = (
`√(87)`)²

x² = (
`√(87)`)² - (
`√(23)`)²

x² = 87 - 23

x² = 64

`√(x)`² =
`√(64)`

x = 8 yd

Answer 2

8

Explanation:

A right angled triangle is made of three sides with the longest side being the hypotenuse. According to pythagoras theorem;

`hyp^(2) = adj^(2)+opp^(2)`

Given hypotenuse =
`√(87)` and another side =
`√(23)`, the third side can be gotten according to the formula above. On substituting;

`(√(87) )^(2) = (√(23) )^(2) + x ^(2) \\x^(2) = (√(87) )^(2) - (√(23) )^(2)\\x^(2) = 87-23\\x^(2) = 64\\x =√(64)\\ x = 8`

The length of the unknown leg in the right triangle is 8