Answer:
x = 10, y ≈ 11.2
Step-by-step explanation:
Hi there,
We can find the length x first since we are given the lengths of the other two sides of the bottom right triangle. In order to find the length of x, it is important to know the Pythagorean Theorem and the fact that x is the hypotenuse.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] ← Pythagorean Theorem
To find x:
[tex]6^{2}[/tex] + [tex]8^{2}[/tex] = [tex]c^{2}[/tex]
100 = [tex]c^{2}[/tex]
c = 10
Therefore, the value of x is 10.
To find y:
We now know the length of two sides of the upper right triangle. The value of y can be found by using the theorem again.
[tex]a^{2}[/tex] + [tex]10^{2}[/tex] = [tex]15^{2}[/tex]
[tex]a^{2}[/tex] + 100 = 225
[tex]a^{2}[/tex] = 125
a = [tex]\sqrt{125}[/tex]
a = 11.2 when rounded to the nearest tenth.
Therefore, the value of y is approximately 11.2.
Hope this explanation is useful. Cheers.
