Question

note: triangle may not be drawn to scale.
suppose ( c = 7 ) and ( a = 45 ) degrees.
find:
( a=)
( b=)
( b=) degrees
give all answers to at least one decimal place. give angles in degrees
question help: video

Explanation:

Step1: Find angle B

In a right - triangle, the sum of angles is \(180^{\circ}\). Since one angle is \(90^{\circ}\) and \(A = 45^{\circ}\), then \(B=180^{\circ}-90^{\circ}-45^{\circ}\).

Step2: Find side a

Using the sine function \(\sin A=\frac{a}{c}\). Given \(c = 7\) and \(A = 45^{\circ}\), so \(a=c\sin A=7\times\sin45^{\circ}=7\times\frac{\sqrt{2}}{2}\approx4.9\).

Step3: Find side b

Using the cosine function \(\cos A=\frac{b}{c}\). Given \(c = 7\) and \(A = 45^{\circ}\), so \(b=c\cos A=7\times\cos45^{\circ}=7\times\frac{\sqrt{2}}{2}\approx4.9\).

Answer:

\(a\approx4.9\)
\(b\approx4.9\)
\(B = 45\) degrees