Question

question 9 of 10
suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60°. what is the length of the third side of the triangle?
a. √3
b. 2√3
c. 2
d. √7

Explanation:

Step1: Recall the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), and \(c\), and the angle \(\theta\) between sides \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\). Here, \(a = 2\), \(b = 3\), and \(\theta=60^{\circ}\), and we need to find \(c\) (the third side).

Step2: Substitute the values into the formula

Substitute \(a = 2\), \(b = 3\), and \(\cos(60^{\circ})=\frac{1}{2}\) into the formula:

$$
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Step3: Find the value of \(c\)

Take the square root of both sides to find \(c\): \(c=\sqrt{7}\) (since length cannot be negative).

Answer:

D. \(\sqrt{7}\)