Question

In ΔABC, if m `/_A` = m`/_C`, m`/_B` = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposite `/_B` ?

A. `sqrt(x^2 - 2x^2 cos beta)`
B. `sqrt(x^2 - (1 - cos beta))`
C. `sqrt(2x^2 (1 - cos beta)^2)`
D. `sqrt(2x^2 (1 - cos beta))`

PLZ HELP!!! 10 Points!!

Answer 1

Answer: D.
`√(2x^2(1-cos) \beta)` is the length of b, the side opposite to
`\angle B`.

Step-by-step explanation:

According to the line of cosines, length of one side when opposite angle and two other sides are given.

c^2=a^2+b^2-2 ab cos C, where a,b, c are the sides of triangle while C is the opposite angle of side c.

Here, a=b=x(because
`\angle A= \angle C`) , c= length of b (that is side AC) and
`C= \angle B= \beta`

Thus,
`AC^2= x^2+x^2-2x*x cos \beta= 2x^2-2x^2cos\beta=2x^2(1-cos\beta) \Rightarrow AC=√(2x^2(1-cos\beta))`

Therefore, length of b =
`√(2x^2(1-cos\beta))`