Question

please I need help
what is the value of x?
a.3√2 b.24 c.12√2 d.8
what is the value of y?
a.4√3 b.√3 c.12 d.10
what is the value of z?
a.12-4√3 b.12 c.6 d.15
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Answer 1

Answer:

x: C

y: A

z:

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is larger than either of the legs by a factor of $\sqrt{2}$. The length of x is therefore:

$12\cdot \sqrt{2}=12\sqrt{2}$

In a 30-60-90 triangle, the longer leg is larger than the shorter leg by a factor of $\sqrt{3}$. Therefore:

$y=\dfrac{12}{\sqrt{3}}=\dfrac{12\sqrt{3}}{3}=4\sqrt{3}$

The hypotenuse of the 30-60-90 triangle is twice larger than the smallest leg, so it has a length of $8\sqrt{3}$.

By the pythagorean theorem, you can find z+y:

$z+y=\sqrt{(12\sqrt{2})^2-12^2}=\sqrt{288-144}=12\\\\4\sqrt{3}+z=12 \\\\z=12-4\sqrt{3}$

Hope this helps!