Question

HELPPPP ME PLZZZZ!!!!!!

Answer 1

Answers:

14. Each leg is
`21√(2)` units long.

15 (a). The longer leg is
`7√(3)` units long

15 (b). The hypotenuse is
`14` units long

=====================================================

Explanations:

For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say

`y = x√(2)` where x is the leg and y is the hypotenuse

Let's solve for x

`y = x√(2)\\\\x√(2) = y\\\\x = (y)/(√(2))\\\\x = (y√(2))/(√(2)*√(2)) \ \text{rationalizing denominator}\\\\x = (y√(2))/(2)\\\\`

Now plug in the given hypotenuse y = 42, this leads to,

`x = (y√(2))/(2)\\\\x = (42√(2))/(2)\\\\x = (42)/(2)√(2)\\\\x = 21√(2)\\\\`

---------------------------

For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.

The longer leg is equal to sqrt(3) times the short leg. The longer leg is
`7√(3)`