*ABC*with m<

*A*= 44,

*C*is a right angle, length of side

*b*= 10. What is the m<

*B*, length of sides

*a*and

*c*?

For a problem such as this we will use trig functions. We know that sine (represented by sin) is the opposite side divided by the hypotenuse.

So sin 44 =

*a*/

*c*. But notice this doesn't help at all since we have 2 unknowns. But we can use cosine (represented as cos) since cosine is adjacent side divided by the hypotenuse.

So cos 44 = 10

*/c*.

Using a scientific calculator we get 0.7193 = 10/

*c*.

Therefore

*c*= 13.9 (rounded to 1 decimal place)

To get the length of side

*a*we could use Pythagorean theorem. But it's best to not use this because if side

*c*(which we just calculated) is incorrect, then the calculation for the length of side a will be incorrect as well.

sin 44 =

*a*/13.9

Using a scientific calculator we get .6947 =

*a*/13.9.

Therefore

*a =*9.7 (rounded to 1 decimal place)

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