Question

question 8 of 10
an isosceles triangle has angle measures 56°, 56°, and 68°. the side across from the 68° angle is 24 cm long. how long are the other sides?
a. 21.5 cm
b. 22.3 cm
c. 18.4 cm
d. 19.9 cm

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let the side opposite the \(68^{\circ}\) angle be \(a = 24\) cm, and the sides opposite the \(56^{\circ}\) angles be \(b\) (we want to find \(b\)). So, \(\frac{a}{\sin A}=\frac{b}{\sin B}\), which becomes \(\frac{24}{\sin68^{\circ}}=\frac{b}{\sin56^{\circ}}\).

Step2: Solve for \(b\)

First, find \(\sin68^{\circ}\approx0.9272\) and \(\sin56^{\circ}\approx0.8290\). Then, from \(\frac{24}{0.9272}=\frac{b}{0.8290}\), we can cross - multiply: \(b=\frac{24\times0.8290}{0.9272}\).
Calculate \(24\times0.8290 = 19.896\), then \(b=\frac{19.896}{0.9272}\approx21.5\)

Answer:

A. \(21.5\) cm