precal question

Question

Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.)

a = 12,    b = 13,    c = 17

∠A =	°
∠B =	°
∠C =	°

Answer 1

a/sinα=b/sinβ=c/sinγ

a^2+b^2-2ab(cosγ)=c^2

144+169-312(cosγ)=289

313-312(cosγ)=289

-312(cosγ)=-24

"/-312 " =-24/-312=.0769....

(cosγ)=.0769........

γ=85.588......º

c/sinγ=17/.997=17.051;

=b/sinβ

=13/sinβ

sinβ=13/17.051

sinβ= .7624....

β=49.679....

180-85.59-49.68=44.73=α

Answer 2

Hi Viviana C

∠A = 44.73° ∠B= 49.68° ∠C = 85.59°

According to Trigonometry when all three sides are known the Law of Cosines can be used to find the cosine of each angle. The Law of Cosines for sides a, b, and c are listed below

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = a² + b² - 2abcosC

Once you've calculated the cosine, then you can use your cos^-1 key on a calculator to find the angle in degrees, whose cosine equals the value you calculated

Give the calculations a try