Finding the Angle

Section 1 of 1

Use the inverse

When you know two sides and want the angle, work out the ratio, then press the inverse ($\sin^{-1}, \cos^{-1}, \tan^{-1}$ — the shift key).

The hypotenuse is $12$ and the opposite side is $8$. Find $A$ to the nearest degree.

Have opp and hyp $\Rightarrow$ $\sin$

$\sin A = \dfrac{8}{12} \Rightarrow A = \sin^{-1}\!\left(\tfrac{8}{12}\right)$

$A = 41.8 = 42^\circ$

$A = 42^\circ$

The opposite side is $3$ and the adjacent side is $8$. Find $A$.

Have opp and adj $\Rightarrow$ $\tan$

$\tan A = \dfrac{3}{8} \Rightarrow A = 20.55 = 21^\circ$

$A = 21^\circ$

The hypotenuse is $43$ and the adjacent side is $21$. Find $A$.

Have adj and hyp $\Rightarrow$ $\cos$

$\cos A = \dfrac{21}{43} \Rightarrow A = 60.7 = 61^\circ$

$A = 61^\circ$

You try

Adjacent $8$, opposite $5$. Find $A$.

$\tan A = \tfrac{5}{8}$.

$A = \tan^{-1}\!\left(\tfrac{5}{8}\right) = 32^\circ$

$A = 32^\circ$

You try

Opposite $7$, adjacent $9$. Find $A$.

$\tan A = \tfrac{7}{9}$.

$A = 37.8 = 38^\circ$

$A = 38^\circ$

You try

Hypotenuse $12$, opposite $9$. Find $A$.

$\sin A = \tfrac{9}{12}$.

$A = 48.5 = 49^\circ$

$A = 49^\circ$

You try

Hypotenuse $9$, opposite $5$. Find $A$.

$\sin A = \tfrac{5}{9}$.

$A = 33.7 = 34^\circ$

$A = 34^\circ$

You try

Opposite $7$, adjacent $6$. Find $A$.

$\tan A = \tfrac{7}{6}$.

$A = 49.3 = 49^\circ$

$A = 49^\circ$

Two sides → the angle, using the inverse key. Class 4: angles of elevation and depression.