Question

I WILL GIVE THE BRAINLEST HURRY PLEASE

Answer 1

Answer:

B) 6

Step-by-step explanation:

It is 45, 45, 90 degrees right triangle, the ratio of the triangle 1:1:√2

Hypotenuse = 3√2*√2

= 3*2

= 6

Thank you.

Answer 2

Answer:

6

Step-by-step explanation:

Hypotenuse is the side that is opposite of the 90 degree angle (the longest side as well).

As seen in the triangle, the side opposite of 45° angle is known AND we want to find the hypotenuse.

Which trigonometric ratio relates opposite with hypotenuse?

SINE

We can write:

$sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{3\sqrt{2}}{h}$

We let hypotenuse be $h$. Also we know that $sin(45)=\frac{1}{\sqrt{2}}$

Now we can solve for $h$:

$sin(45)=\frac{3\sqrt{2}}{h}\\h*sin(45)=3\sqrt{2}\\h=\frac{3\sqrt{2}}{sin(45)}\\h=\frac{3\sqrt{2}}{\frac{1}{\sqrt{2}}}\\h=3\sqrt{2}*\frac{\sqrt{2}}{1}\\h=6$

(we used the identity $(\sqrt{a})(\sqrt{a})=a$)

2nd answer choice is right. Hypotenuse is 6.