Question

HELPPPP ME PLZZZZ!!!!!!

Answer 1

Answers:

14.  Each leg is   $21\sqrt{2}$  units long.

15 (a). The longer leg is $7\sqrt{3}$  units long

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

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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

$y = x\sqrt{2}$ where x is the leg and y is the hypotenuse

Let's solve for x

$y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}$

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

$x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}$

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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 $7\sqrt{3}$