Question

What is the length of AC¯¯¯¯¯ ?

Answer 1

AC = 12.38 cm

Explanation:

We are given a triangle ABC with two known angles and one known side length and we are to find the length of another side AC.

For this, we can use the sine rule and its formula is given by:

`\frac {a} {sin (A) } = \frac {b} {sin (B) }`

Substituting the given values in the above formula:

`\frac {13} {sin(85.2)} = \frac {AC} {sin(71.6)}`

`AC = \frac {13} {sin(85.2)} * sin (71.6)`

AC = 12.38 cm

Answer 2

AC = 12.38 cm

Explanation:

When there are 2 pairs given, we can use the sine rule to solve the problem.

By pairs we mean "an angle and side opposite to it"

1 pair is 85.2 degree angle and 13 cm, and another pair is 71.6 degree angle and the side AC (which we want to figure out).

Sine Rule is given by
`(SinA)/(a)=(SinB)/(b)`

where,

A and B are the two respective angles and a and b are the two respective sides (of the pairs). Plugging all the info and using algebra, we have:

`(Sin85.2)/(13)=(Sin71.6)/(AC)\\AC*Sin85.2=13*Sin71.6\\AC=(13*Sin71.6)/(Sin85.2)\\AC=12.38`

Thus, AC = 12.38 cm