Question

score on last try: 0 of 1 pt. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. next question get a similar question you can retry this question below note: triangle may not be drawn to scale. suppose a = 10 and a = 60 degrees. find: b = c = b = degrees give all answers to at least one decimal place. give angles in degrees question help: video submit question

Explanation:

Step1: Find angle B

In a right triangle, the sum of angles is \(180^\circ\), and one angle is \(90^\circ\). So \(B = 180^\circ - 90^\circ - 60^\circ = 30^\circ\).

Step2: Find side b using tangent

\(\tan(A)=\frac{a}{b}\), so \(b=\frac{a}{\tan(A)}\). Substituting \(a = 10\) and \(A = 60^\circ\), \(\tan(60^\circ)=\sqrt{3}\), so \(b=\frac{10}{\sqrt{3}}\approx5.8\).

Step3: Find side c using sine

\(\sin(A)=\frac{a}{c}\), so \(c=\frac{a}{\sin(A)}\). \(\sin(60^\circ)=\frac{\sqrt{3}}{2}\), so \(c=\frac{10}{\frac{\sqrt{3}}{2}}=\frac{20}{\sqrt{3}}\approx11.5\).

Answer:

\(b\approx5.8\), \(c\approx11.5\), \(B = 30.0\) degrees