Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c = 289.8 \mathrm {~cm} , \angle A = 24.62 ^ { \circ }$$
A) a = 632.4 cm, b = 132.8 cm
B) a = 695.6 cm, b = 632.4 cm
C) a = 120.7 cm, b = 263.5 cm
D) a = 181.2 cm, b = 226.2 cm
E) a = 318.8 cm, b = 695.6 cm

Question

Find the unknown sides of the right triangle (see illustration). Round your answer to the appropriate number of significant digits. $$c = 289.8 \mathrm {~cm} , \angle A = 24.62 ^ { \circ }$$ 
A) a = 632.4 cm, b = 132.8 cm 
B) a = 695.6 cm, b = 632.4 cm 
C) a = 120.7 cm, b = 263.5 cm 
D) a = 181.2 cm, b = 226.2 cm 
E) a = 318.8 cm, b = 695.6 cm

Quizplus · Accepted Answer

We can use the trigonometric ratios to solve for the unknown sides.

Let's start with finding side $a$.

$	an \angle A = \frac{a}{c}$

$\Rightarrow a = c 	an \angle A$

$\Rightarrow a = 289.8 \mathrm{~cm} \cdot 	an 24.62^\circ$

$\Rightarrow a \approx 120.7 \mathrm{~cm}$

Now, to find side $b$:

$\sin \angle A = \frac{b}{c}$

$\Rightarrow b = c \sin \angle A$

$\Rightarrow b = 289.8 \mathrm{~cm} \cdot \sin 24.62^\circ$

$\Rightarrow b \approx 263.5 \mathrm{~cm}$

Therefore, the best choice is C, where $a = 120.7 \mathrm{~cm}$ and $b = 263.5 \mathrm{~cm}$.

Find the Unknown Sides of the Right Triangle (See Illustration) c=289.8 cm,∠A=24.62∘c = 289.8 \mathrm {~cm} , \angle A = 24.62 ^ { \circ }c=289.8 cm,∠A=24.62∘

Find the Unknown Sides of the Right Triangle (See Illustration) $c = 289.8 \mathrm {~cm} , \angle A = 24.62 ^ { \circ }$