If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation?
1 answer:
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Answer:
x = 14
y = 14
z= 14
Step-by-step explanation:
Notice that the top triangle is a 45-45-90 triangle and the triangle below is a 30-60-90 triangle.
Using the fact that the top triangle is a 45-45-90 triangle and also an isosceles triangle, we can see that <em>x</em> will be the same as its respective leg, 14
Now, we must find a side length of the bottom triangle. We can use the Pythagorean Theorem to find the third side of the top triangle, which is also a side of the bottom triangle. We can find that the third side must be 28. We can now use this to find the other sides of the bottom triangle.
Since <em>y</em> is opposite to the 30 degree angle, it is half of the hypotenuse. The hypotenuse which we found earlier is 28, therefore, <em>y</em> is 14. <em>z </em>is then 14 using either Pythagorean Theorem or special right triangle properties for 30-60-90.