Question

question 1 of 10
a triangle has two angles measuring 26° and 93°. the side across from the third angle is 23 units long. what are the lengths of the other two sides?
a. 11.5
b. 10.1
c. 52.4
d. 26.3

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(C\). Then \(C = 180-(26 + 93)=61^{\circ}\).

Step2: Use the Law of Sines

The Law of Sines states \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let the side opposite \(26^{\circ}\) be \(a\), opposite \(93^{\circ}\) be \(b\), and opposite \(61^{\circ}\) (\(c = 23\)).
For \(a\): \(\frac{a}{\sin26}=\frac{23}{\sin61}\), so \(a=\frac{23\sin26}{\sin61}\approx11.5\).
For \(b\): \(\frac{b}{\sin93}=\frac{23}{\sin61}\), so \(b=\frac{23\sin93}{\sin61}\approx26.3\).

Answer:

A. 11.5, D. 26.3