Question

20.) A=49.23 degrees, c=54.8Solve the right triangle. Express angles in decimal degrees.

Answer 1

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

Explanation

Step 1

a) let

$\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}$

b) b value

to find the measure of side b we can use cosine function

$\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}$

c) angle B

to find the measure of Angle B we can use sine function

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}$

d) side a

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}$

so, the answer is

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

I hope this helps you