Question

note: triangle may not be drawn to scale.
suppose c = 8 and a = 45 degrees.
find:
a =
b =
b = degrees
give all answers to at least one decimal place. give angles in degrees

Explanation:

Step1: Find angle B

Sum of angles in a triangle is \(180^{\circ}\).
\(B = 180^{\circ}-90^{\circ}-A\)
Substitute \(A = 45^{\circ}\)
\(B=180^{\circ}-90^{\circ}-45^{\circ}=45^{\circ}\)

Step2: Find side a

Using \(\sin A=\frac{a}{c}\)
\(a = c\times\sin A\)
Substitute \(c = 8\) and \(A = 45^{\circ}\) (\(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\))
\(a = 8\times0.707 = 5.656\approx5.7\)

Step3: Find side b

Using \(\cos A=\frac{b}{c}\)
\(b = c\times\cos A\)
Substitute \(c = 8\) and \(A = 45^{\circ}\) (\(\cos45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\))
\(b = 8\times0.707 = 5.656\approx5.7\)

Answer:

\(a = 5.7\)
\(b = 5.7\)
\(B = 45.0\) degrees