Question

PLEASE OF YOU CAN SHOW THE WORK:

Answer 1

Answer:

$x\approx24^\circ$

Step-by-step explanation:

We know that r and s have a combined length of 70. Therefore:

$r+s=70$

Notice that we can determine r by using the Pythagorean Theorem. In this case, r is the hypotenuse, and 20 and 8 are the legs. Therefore:

$a^2+b^2=c^2$

Substituting 20 and 8 for a and b and r for c yields:

$20^2+8^2=r^2$

Compute:

$464=r^2$

Therefore:

$r=\sqrt{464}=\sqrt{16\cdot 29}=4\sqrt{29}$

Now, we can determine s. We know that:

$s+r=70$

So, by substitution:

$s+4\sqrt{29}=70$

Therefore:

$s=70-4\sqrt{29}$

Now, notice that, with respect to x, 20 is the opposite side and s is the hypotenuse.

Therefore, we can use the sine ratio. The sine ratio is the ratio between a right triangles opposite side to its hypotenuse.

In this case, the opposite to x is 20, and the hypotenuse is s, or 70-4√29. Therefore:

$\displaystyle \sin(x^\circ)=\frac{20}{s}$

By substitution:

$\displaystyle \sin(x^\circ)=\frac{20}{70-4\sqrt{29}}$

Take the inverse sine of both sides:

$\displaystyle x^\circ=\sin^{-1}\Big(\frac{20}{70-4 \sqrt{29}} \Big)$

Use a calculator. Therefore:

$x\approx24.37^\circ\approx24^\circ$