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# Determine the value of a:

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Determine the value of a:

Apr 19, 2020

#1
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Hi guest!

So for this problem, we can connect WY so that we have 2 right triangles, $$\triangle WXY \text { and } \triangle WYZ$$

(Just in case you don't know why $$\triangle WYZ$$ is a right triangle, it's because $$\triangle WXY$$ is a 45-45-90 triangle (since it has equal legs) and 135-45=90.)

First, let's find WY. Triangle WXY is a right triangle, so using the Pythagorean theorem, $$WY=4\sqrt{2}$$

Now we know the 1 leg and the hypotenuse of $$\triangle WYZ$$! From here, we can just use the Pythagorean theorem.

$$a^2+(4\sqrt2)^2=9^2$$

$$a^2+32=81$$

$$a^2=49$$

$$\boxed{a=7}$$

I hope this helped you, guest!

:)

Apr 19, 2020