A triangle has sides A, B, and C. Sides A and B are of lengths $2$ $2$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{π}{4}$ $pi/4$ . What is the length of side C?

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Answer 1 · 2016-09-27T21:16:01

$:. C=~~3.855.$

We use the Cosine-Rule for $DeltaABC$ , which states,

$C^2=A^2+B^2-2ABcos(/_(A,B)),$

where, by " $/_(A,B)$ , we mean the angle btwn. sides $A & B.$ .

$:. C^2=2^2+5^2-2*2*5cos(pi/4)$

$=29-20(1/sqrt2)=29-10sqrt2$

$~~29-10(1.414)=29-14.14=14.86$

$:. C~~3.855$

A triangle has sides A, B, and C. Sides A and B are of lengths 222 and 555, respectively, and the angle between A and B is pi/4π4pi/4. What is the length of side C?