Question

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

Explanation:

Step1: Find angle C

In a triangle, the sum of interior angles is \(180^\circ\). So, \(\angle C = 180^\circ - 98^\circ - 45^\circ = 37^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{AB}{\sin C}=\frac{BC}{\sin A}\). We know \(BC = 15\), \(\angle A = 98^\circ\), \(\angle C = 37^\circ\). So, \(AB=\frac{BC\times\sin C}{\sin A}\).
Substitute the values: \(AB=\frac{15\times\sin 37^\circ}{\sin 98^\circ}\).
We know \(\sin 37^\circ\approx0.6018\), \(\sin 98^\circ\approx0.9903\).
Then \(AB=\frac{15\times0.6018}{0.9903}\approx\frac{9.027}{0.9903}\approx9.1\).

Answer:

\(9.1\)