Answer:
10.3 cm
Explanation:
There are a few ways to do this.
1)
Using the law of cosines, you have ...
b² = a² +c² -2ac·cos(B)
b² = 11² +11² -2(11)(11)·cos(56°) = 106.67
b = √106.675 ≈ 10.3
AC = 10.3 cm
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2)
Using trig functions. When you draw an altitude in this isosceles triangle from B to AC, it divides AC in half, and it divides angle B in half. The sine relation can help here:
Sin = Opposite/Adjacent
sin(56°/2) = (AC/2)/(11 cm)
AC = (22 cm)sin(28°) ≈ 10.3 cm
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3)
Using a triangle solver, you can find the value of AC to be about 10.3 cm. Triangle solvers are available as apps and on the web. Your graphing calculator may have one. See attached for the results from a nice solver available on the web. Units are cm.