Question

What is the value of a?

Answer 1

Answer:

a = 15

Step-by-step explanation:

The Law of Cosines

a^2 = 13^2 + 14^2 - 2(13)(14)Cos(67.4)

a^2 = 169 + 196 - (364 * 0.3843)

a^2 = 365 -140

a^2 = 225

a = 15

Answer 2

For this case, we have by definition the law of cosine states that:

$a = \sqrt {b ^ 2 + c ^ 2-2 (b) (c) * cosine (67.4)}$

We have to:

$b = 13\\c = 14$

Substituting:

$a = \sqrt {13 ^ 2 + 14 ^ 2-2 (13) (14) * cosine (67.4)}\\a = \sqrt {169 + 196-364 * 0.38429532}\\a = \sqrt {365-139.8834965}\\a = \sqrt {225.1165035}\\a = 15.00388295$

Rounding off we have:

$a = 15$

Answer:

$a = 15$