Question

If A=16°55’ and c=13.7, find a (picture provided)

Answer 1

C

Explanation:

Use the definition of the sine function:

`\sin \angle A=\frac{\text{opposite leg}}{\text{hypotenuse}}=(BC)/(AB).`

Substitute
`\angle A=16^(\circ)55'` and
`c=13.7` into the previous formula:

`\sin 16^(\circ)55'=(a)/(c),\\ \\\sin 16^(\circ)55'=(a)/(13.7),\\ \\a=13.7\cdot \sin16^(\circ)55',\\ \\a\approx 13.7\cdot 0.284\approx 4`

Answer 2

c. 4.0

Explanation:

To find a, we'll use the Law of Sines that says:

`(a)/(sin(A)) = (c)/(sin(C))`

And we'll isolate a to get:

`a = (sin(A) * c)/(sin(C))`

Then we will plug-in the information we already have (changing 16°55' into 16.92)

`a = (sin(16.92) * 13.7)/(sin(90)) = 3.99`

So, let's round it to 4 to match the answer number C.