A 45-45-90 right triangle is isosceles. That means both legs are the same length, and its hypotenuse is √2 times the leg length. You can figure these facts using trigonometry or the Pythagorean theorem, or you can rely on your memory of them.

w = 8 . . . . . . . . . . . same as the leg length shown

x = y = 8√2 . . . . . hypotenuse of smaller triangle; both legs are the same

z = (8√2)√2 = 16 . . . . hypotenuse of larger triangle

3 0

3 years ago

What is the exact value of sin 45° ? enter your answer, as a simplified fraction.

Ne4ueva [31]

Look at the picture.

Use the Pythagorean theorem:

$b^2=a^2+a^2\\\\b^2=2a^2\to b=\sqrt{2a^2}\\\\b=\sqrt{a^2}\cdot\sqrt2\\\\b=a\sqrt2$

$\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=45^o,\ opposite=a,\ hypotenuse=a\sqrt2$

substitute

$\sin45^o=\dfrac{a}{a\sqrt2}=\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}=\dfrac{\sqrt2}{2}$

Answer: $\sin45^o=\dfrac{\sqrt2}{2}$

7 0

3 years ago

2(2x + 7) = 2 + 2x A. One Solution B. No Solution C. Infinite Solutions

Rudik [331]

B. I am so sorry if it is not right

5 0

3 years ago

Read 2 more answers

A university hired you as a lab assistant after you graduated. Your starting salary is $41,500 and your salary will increase by

VladimirAG [237]

Answer:

$67,000

Step-by-step explanation:

41,000*(1,700*15)=67,000

5 0

3 years ago