# How do you solve the right triangle given A=52 degrees and B=8.4?

See solution below

#### Explanation:

The sum of other two acute angles in a right $\setminus \triangle A B C$ is ${90}^{\setminus} \circ$

$\setminus \angle A + \setminus \angle C = {90}^{\setminus} \circ$

$\setminus \angle C = {90}^{\setminus} \circ - \setminus \angle A$

$= {90}^{\setminus} \circ - {52}^{\setminus} \circ$

$= {38}^{\setminus} \circ$

Given that hypotenuse $B$ of right $\setminus \triangle A B C$ is $8.4$

Now, using sine rule in right $\setminus \triangle A B C$

$\setminus \frac{A}{\setminus \sin \setminus \angle A} = \setminus \frac{B}{\setminus \sin \setminus \angle B} = \setminus \frac{C}{\setminus \sin \setminus \angle C}$

$\setminus \frac{A}{\setminus \sin {52}^{\setminus} \circ} = \setminus \frac{8.4}{\setminus \sin {90}^{\setminus} \circ} = \setminus \frac{C}{\setminus \sin {38}^{\setminus} \circ}$

$A = 8.4 \setminus \sin {52}^{\setminus} \circ = 6.619$

$C = 8.4 \setminus \sin {38}^{\setminus} \circ = 5.171$