Question

If B=16°45’ and c=13 then find a (picture provided)

Answer 1

The length of side marked a is 12.4 units.

Explanation:

In ΔABC

∠B = 16°45’ = 16.75°

1 min arc =
`(1)/(60) degrees`

c = 13 units

a = ?

`\cos \theta=(Base)/(Hypotenuse)`

`\cos B=(a)/(13)`

`0.95757=(a)/(13)`

`a=0.95757* 13=12.4484\approx 12.4 units`

The length of side marked a is 12.4 units.

Answer 2

A. 12.4

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))`

We first need to find A, which is easy. The sum of the interior angles of a triangle is 180 degrees... and we already have 2 of them, so:

A = 180 - 90 - 16.75 = 73.25

(converted 16°45' to 16.75)

Then we will plug-in the information we already have

`c = (sin(73.25) * 13)/(sin(90)) = 12.45`

So, let's round it to 12.4 to match the answer A.