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PLEASE HELP.

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?

PLEASE HELP. Consider ABC with the measure of angle B equal to 60 degrees, and side-example-1
User Bouba
by
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2 Answers

2 votes

Answer:

(B)
b=√(25+16-20)

Explanation:

It is given that we have to consider triangle ABC in which ∠B=60° and the side lengths are a=4 and c=5.

Therefore, in order to find the value of the side length b, we will use the Law of Cosines that is:


b^2=c^2+a^2-2(c)(a)cosB

substituting the given values, we get


b^2=(5)^2+(4)^2-2(5)(4)cos60^(\circ)


b^2=25+16-40((1)/(2))


b^2=25+16-20


b=√(25+16-20)

which is the required side length of b.

Thus, option B is correct.

User Ghanshyam Nakiya
by
7.9k points
5 votes
we know that
the law of cosines establish
b²=a²+c²-2*a*c*cos B
in this problem
a=4 units
c=5 units
B=60°
so
b²=a²+c²-2*a*c*cos B
b²=4²+5²-2*4*5*cos 60°
b²=16+25-40*(1/2)
b²=16+25-20
b=√[16+25-20]

the answer is
b=√[16+25-20]

User John Reilly
by
8.3k points

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