Question

the following figure shows △abc with side lengths to the nearest tenth. find ac in △abc. round to the nearest tenth. ac =

Explanation:

Step1: Find angle C

In a triangle, the sum of interior angles is \(180^\circ\). So, \(\angle C=180^\circ - 125^\circ - 29^\circ = 26^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{AC}{\sin B}=\frac{BC}{\sin A}\). We know \(BC = 7\), \(\angle B = 29^\circ\), \(\angle A=125^\circ\). So, \(AC=\frac{BC\times\sin B}{\sin A}\).
Substitute the values: \(AC=\frac{7\times\sin29^\circ}{\sin125^\circ}\).
Calculate \(\sin29^\circ\approx0.4848\), \(\sin125^\circ=\sin(180^\circ - 55^\circ)=\sin55^\circ\approx0.8192\).
Then \(AC=\frac{7\times0.4848}{0.8192}\approx\frac{3.3936}{0.8192}\approx4.1\).

Answer:

\(4.1\)