Question

note: triangle may not be drawn to scale.
suppose a = 2 and a = 70 degrees.
find:
b =
c =
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 \( A + B+90^{\circ}=180^{\circ} \). So \( B = 180^{\circ}-90^{\circ}-A \).
Substitute \( A = 70^{\circ} \), then \( B=20^{\circ} \).

Step2: Find side \( b \)

Use the tangent function \( \tan(A)=\frac{a}{b} \). So \( b=\frac{a}{\tan(A)} \).
Given \( a = 2 \) and \( A = 70^{\circ} \), \( \tan(70^{\circ})\approx2.747 \), then \( b=\frac{2}{\tan(70^{\circ})}\approx0.7 \).

Step3: Find side \( c \)

Use the sine function \( \sin(A)=\frac{a}{c} \). So \( c=\frac{a}{\sin(A)} \).
Given \( a = 2 \) and \( A = 70^{\circ} \), \( \sin(70^{\circ})\approx0.940 \), then \( c=\frac{2}{\sin(70^{\circ})}\approx2.1 \).

Answer:

\( b = 0.7 \), \( c = 2.1 \), \( B = 20.0 \) degrees