Question

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. /7
C. 2 /3
D. 2

Answer 1

Answer:

$\text{The length of third side is }\sqrt7 units$

Step-by-step explanation:

Given that a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60°.

Let b=2 units and c=3 units

we have to find the length of the third side of the triangle.

By law of cosines

$a^2=b^2+c^2-2bc\cosA$

where A is the angle between the side b and c

$a^2=2^2+3^2-2(2)(3)\cos60$

$a^2=4+9-6=7$

$a=\pm\sqrt7$

Length cannot be negative

∴ $a=\sqrt7 units$

Option B is correct.

Answer 2

There is a photo with equations and the answer.