# How do you solve the right triangle given a = 84cm, A=35 degrees?

side $c = 146.4495308 \text{ }$centimeters
side $b = 119.9644326 \text{ }$centimeters
Angle $B = {55}^{\circ}$
Area $= 5038.506169 \text{ }$square cm
Perimeter$= 350.4139634 \text{ }$centimeters

#### Explanation:

From the given data:
Angle $C = {90}^{\circ}$
Angle $A = {35}^{\circ}$
side $a = 84 \text{ }$cm

To solve for Angle B:

$B = {90}^{\circ} - A = {90}^{\circ} - {35}^{\circ} = {55}^{\circ}$

To solve for side $c$

$\sin A = \frac{a}{c}$

$c = \frac{a}{\sin} A = \frac{84}{\sin {35}^{\circ}} = 146.4495308 \text{ }$cm

To solve for side $b$

$\tan A = \frac{a}{b}$

$b = \frac{a}{\tan} A = \frac{84}{\tan {35}^{\circ}} = 119.9644326 \text{ }$cm

To solve for the Area:

Area$= \frac{1}{2} \cdot b \cdot a = \frac{1}{2} \cdot 119.9644326 \cdot 84 = 5038.506169 \text{ }$square cm

To solve for the Perimeter P:

$P = a + b + c = 84 + 119.9644326 + 146.4495308$
$P = 350.4139634 \text{ }$cm

God bless....I hope the explanation is useful.