Question

I been working I can’t seem to find the answer and I get it mixed up with algebra

Answer 1

A. 10.6

1) In this problem, we have a right triangle. We know two angles and one length of the hypotenuse. If we pay attention to that triangle, we can see that this is an isosceles triangle.

2) So, we can find the missing leg making use of the Pythagorean theorem or we can use trig ratios.

`\begin{gathered} a^2=b^2+c^2 \\ 15^2=x^2+x^2 \\ 225=2x^2 \\ (225)/(2)=(2x^2)/(2) \\ x^2=112.5 \\ x\approx10.6 \\ \\ or \\ \\ \sin (45)=(x)/(15) \\ \frac{\sqrt[]{2}}{2}=(x)/(15) \\ 2x=15\sqrt[]{2} \\ x=\frac{15\sqrt[]{2}}{2} \\ x\approx10.6 \end{gathered}`

Note that either way we can find the same result. So the answer is 10.6