Question

chapter 5 review score: 10/100 answered: 1/10 question 10 note: triangle may not be drawn to scale. suppose c = 15 and a = 40 degrees. find: a = b = b = degrees give all answers to at least one decimal place. give angles in degrees question help: post to forum submit question

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the interior angles is 180 degrees. Since one angle is 90 degrees and A = 40 degrees, we can find B.
$B=180 - 90 - A$
$B = 180-90 - 40=50$ degrees

Step2: Find side a

We use the sine function. $\sin(A)=\frac{a}{c}$. Given $c = 15$ and $A = 40$ degrees.
$a=c\times\sin(A)$
$a = 15\times\sin(40^{\circ})\approx15\times0.643\approx9.6$

Step3: Find side b

We use the cosine function. $\cos(A)=\frac{b}{c}$. Given $c = 15$ and $A = 40$ degrees.
$b=c\times\cos(A)$
$b = 15\times\cos(40^{\circ})\approx15\times0.766\approx11.5$

Answer:

$a\approx9.6$
$b\approx11.5$
$B = 50.0$ degrees