Question

Find x (picture included)

Answer 1

In order to solve for 'x', we have to use trigonometry

(Bear with me, it's not that bad)

Always remember "SOH CAH TOA." This'll definitely help you figure out when you should use sin ($\frac{Opposite}{Hypotenuse}$), cosine($\frac{Adjacent}{Hypotenuse}$), or tangent($\frac{Opposite}{Adjacent}$).

In this scenario, we could use cos(57) but using sin(33) is way easier and more practical.

sin(33) = $\frac{7.9}{x}$

Recall that sin is opposite/hypotenuse.

Whip out your calculator and find the value of sin(33)

(A side note: If you're going to use the internet as a calculator, be sure to include "deg" at the end of your equation so that it solves correctly. In this case, type in "sin33 deg." This ensures that the calculator isn't solving your equation in radians, which is the default.)

Anyway:

0.5446 = $\frac{7.9}{x}$

Cross multiply:

0.5446x = 7.9

To isolate x, divide both sides by 0.5446:

x = $\frac{7.9}{0.5446}$

Whip out your fancy calculator one more time (unless you have the willpower to solve this by hand, I don't)

x = 14.5061

Huzzah! We're finally done! That wasn't too bad, wasn't it?

Note that all of my calculations are rounded, if you needed a specific number of significant figures, tell me and I'll fix it :)

Good luck!