Question

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

Answer 1

Answer:

The length of side marked a is 12.4 units.

Step-by-step explanation:

In ΔABC

∠B = 16°45’ = 16.75°

1 min arc = $\frac{1}{60} degrees$

c = 13 units

a = ?

$\cos \theta=\frac{Base}{Hypotenuse}$

$\cos B=\frac{a}{13}$

$0.95757=\frac{a}{13}$

$a=0.95757\times 13=12.4484\approx 12.4 units$

The length of side marked a is 12.4 units.

Answer 2

Answer:

A. 12.4

Step-by-step explanation:

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

$\frac{a}{sin(A)} = \frac{c}{sin(C)}$

And we'll isolate a to get:

$a = \frac{sin(A) * c}{sin(C)}$

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

$c = \frac{sin(73.25) * 13}{sin(90)} = 12.45$

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