Question

question 4
note: triangle may not be drawn to scale.
suppose a = 2 and a = 15 degrees.
find:
b =
c =
b = degrees
give all answers to at least one decimal place. give angles in degrees

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the non - right angles is \(90^{\circ}\). So \(B = 90^{\circ}-A\). Given \(A = 15^{\circ}\), then \(B=90 - 15=75^{\circ}\).

Step2: Find side b using tangent function

We know that in a right - triangle, \(\tan(A)=\frac{a}{b}\), so \(b=\frac{a}{\tan(A)}\). Given \(a = 2\) and \(A = 15^{\circ}\), \(\tan(15^{\circ})\approx0.2679\). Then \(b=\frac{2}{\tan(15^{\circ})}=\frac{2}{0.2679}\approx7.5\) (rounded to one decimal place).

Step3: Find side c using sine function

We know that \(\sin(A)=\frac{a}{c}\), so \(c=\frac{a}{\sin(A)}\). \(\sin(15^{\circ})\approx0.2588\). Given \(a = 2\), then \(c=\frac{2}{\sin(15^{\circ})}=\frac{2}{0.2588}\approx7.7\) (rounded to one decimal place).

Answer:

\(b\approx7.5\), \(c\approx7.7\), \(B = 75.0\) degrees