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

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

where A is the angle between the side b and c

Length cannot be negative

∴

Option B is correct.

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.