Question

solve the triangle. round to one decimal places.

a. c = 103°, a = 17.5 m, b = 9.9 m
b. c = 97°, a = 9.7 m, b = 17.2 m
c. c = 103°, a = 9.9 m, b = 17.5 m
d. c = 103°, a = 48.9 m, b = 27.6 m

Explanation:

Step1: Find angle \( C \)

Sum of angles in a triangle is \( 180^{\circ} \).
\( C=180^{\circ}-(26^{\circ} + 51^{\circ})=103^{\circ} \)

Step2: Use the Law of Sines (\( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \))

Given \( c = 22\) m, \(A = 26^{\circ}\), \(B=51^{\circ}\), \(C = 103^{\circ}\)
For \(a\): \(\frac{a}{\sin26^{\circ}}=\frac{22}{\sin103^{\circ}}\), so \(a=\frac{22\times\sin26^{\circ}}{\sin103^{\circ}}\)
\(\sin26^{\circ}\approx0.4384\), \(\sin103^{\circ}\approx0.9744\)
\(a=\frac{22\times0.4384}{0.9744}\approx9.9\) m
For \(b\): \(\frac{b}{\sin51^{\circ}}=\frac{22}{\sin103^{\circ}}\), so \(b=\frac{22\times\sin51^{\circ}}{\sin103^{\circ}}\)
\(\sin51^{\circ}\approx0.7771\), \(\sin103^{\circ}\approx0.9744\)
\(b=\frac{22\times0.7771}{0.9744}\approx17.5\) m

Answer:

C. \( C = 103^{\circ},a = 9.9\) m, \(b = 17.5\) m