Question

using the information given about the triangle show what is the length of (overline{bc}) to the nearest tenth?

8 of 12 questi

12.5 in

10.8 in

11.5 in

12.9 in

Explanation:

Step1: Find angle \( C \)

Sum of angles in a triangle is \( 180^{\circ} \). So \( \angle C=180^{\circ}-(70^{\circ} + 64^{\circ})=46^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines is \( \frac{BC}{\sin A}=\frac{AC}{\sin B} \). Here \( A = 70^{\circ} \), \( AC = 12 \) in, \( B=64^{\circ} \).
Substitute into the formula: \( BC=\frac{12\times\sin70^{\circ}}{\sin64^{\circ}} \)
We know that \( \sin70^{\circ}\approx0.9397 \), \( \sin64^{\circ}\approx0.8988 \)
Then \( BC=\frac{12\times0.9397}{0.8988}=\frac{11.2764}{0.8988}\approx12.5 \)

Answer:

12.5 in