Question

question 8
note: triangle may not be drawn to scale.
suppose c = 14 and a = 30 degrees.
find:
a =
b =
b = degrees
give all answers to at least one decimal place. give angles in degrees
add work

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Explanation:

Step1: Find side a using sine function

We know that $\sin(A)=\frac{a}{c}$. Given $c = 14$ and $A=30^{\circ}$, so $a = c\times\sin(A)$. Substituting the values, we get $a=14\times\sin(30^{\circ})=14\times0.5 = 7$.

Step2: Find side b using cosine function

We know that $\cos(A)=\frac{b}{c}$. So $b = c\times\cos(A)$. Substituting $c = 14$ and $A = 30^{\circ}$, we have $b=14\times\cos(30^{\circ})=14\times\frac{\sqrt{3}}{2}=7\sqrt{3}\approx 12.1$.

Step3: Find angle B

Since the sum of angles in a triangle is $180^{\circ}$ and one angle is $90^{\circ}$ and $A = 30^{\circ}$, then $B=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$.

Answer:

$a = 7$
$b\approx12.1$
$B = 60$