Question

Find c to the nearest 10th. (laws of sines)

Answer 1

Option D

Explanation:

By applying cosine rule in the given triangle,

a² = b² + c² - 2b.c.cos(m∠A)

By substituting values in the formula,

9² = 10² + c² - 2(10)(c)cos(15)°

81 = 100 + c² - 19.32c

c² - 19.31c + 19 = 0

By quadratic formula,

c =
`\frac{19.31\pm\sqrt{(19.31)^(2)-4(1)(19)}}{2(1)}`

=
`(19.31\pm17.23)/(2)`

= 1.08, 18.27

≈ 1.1, 18.3

Therefore, Option D will be the answer.