Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

For this case we can use the law of cosine to determine the length of side b.
We have then:
b ^ 2 = a ^ 2 + c ^ 2 - 2 * a * c * cos (B)
Substituting values we have:
b ^ 2 = 4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60)
Clearing b:
b = root (4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60))
Answer:
an expression that is equivalent to the length of side b is:
b = root (4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60))

Answer Link

jajumonac jajumonac · Answer 2 · 2020-03-15T02:10:39+01:00

Answer:

[tex]b=\sqrt{25+16-20}[/tex]

Step-by-step explanation:

(The choices are attached)

We don't if the triangle ABC is a right triangle of other kind, that's why we need to use the cosines law which is defined as

[tex]b^{2}=a^{2} +c^{2}-2.a.c.cosB\°[/tex]

Where [tex]a=4[/tex] [tex]c=5[/tex] and [tex]B=60\°[/tex], replacing these values we have

[tex]b^{2}=4^{2}+5^{2}-2(4)(5)cos(60\°)\\ b=\sqrt{16+25-40\frac{1}{2} }\\ b=\sqrt{25+16-20}[/tex]

Remember that [tex]cos60\°=\frac{1}{2}[/tex]

Therefore, the second choice is the correct answer

[tex]b=\sqrt{25+16-20}[/tex]