When x is Underneath

Section 1 of 1

x on the bottom

If the unknown is the bottom of the fraction, swap it with the ratio: $x = \dfrac{\text{side you have}}{\text{ratio of the angle}}$.

The opposite side is $5$ and the angle is $33^\circ$. Find the hypotenuse $x$.

Have opp, want hyp $\Rightarrow$ $\sin$

$\sin 33 = \dfrac{5}{x} \Rightarrow x = \dfrac{5}{\sin 33}$

$x = 9.18 = 9.2$

$x = 9.2$

The adjacent side is $12$ and the angle is $39^\circ$. Find the hypotenuse $x$.

Have adj, want hyp $\Rightarrow$ $\cos$

$\cos 39 = \dfrac{12}{x} \Rightarrow x = \dfrac{12}{\cos 39}$

$x = 15.44 = 15.4$

$x = 15.4$

The opposite side is $6$ and the angle is $47^\circ$. Find the adjacent side $x$.

Have opp, want adj $\Rightarrow$ $\tan$

$\tan 47 = \dfrac{6}{x} \Rightarrow x = \dfrac{6}{\tan 47}$

$x = 5.59 = 5.6$

$x = 5.6$

You try

Opposite $5$, angle $43^\circ$. Find the hypotenuse $x$.

$x = \dfrac{5}{\sin 43}$.

$x = \dfrac{5}{\sin 43} = 7.33 = 7.3$

$x = 7.3$

You try

Adjacent $8$, angle $23^\circ$. Find the hypotenuse $x$.

$x = \dfrac{8}{\cos 23}$.

$x = \dfrac{8}{\cos 23} = 8.7$

$x = 8.7$

When $x$ is on the bottom, divide. Class 3: finding the angle itself.