Question

Can someone tell me if I did this right? Given b = 12, c = 15 and A = 60° in triangle ABC, use the Law of Cosines to solve for a. Fill in the blank(s) to complete each step. If applicable, be sure to enter all decimal numbers with a zero in the ones place. Round your final answer to the nearest hundredth.

Answer 1

a^2= b^2+c^2 - 2bc.cosA

a^2= (12)^2 + (15)^2 - 2 x 12 x 15 cos60

a^2= 144+225 - 2 x 12 x 15 x 0.5

a^2 = 369 - 180

a^2= 189
now take the square root of both sides.. :)

so a = 13.74 :)

Answer 2

a=13.74 units

Explanation:

Given are two sides and angle of a triangle ABC

use cosine formula for triangles

`a^2=b^2+c^2-2bccosA\\=144+225-360(0.5)\\=369-180\\=189`

Now we got the square of the third side

Take square root and round off to two decimals to get exact value of a

a =13.74 units

Note: In a triangle, if 3 independent dimensions are known we can find out all missing sides and angles using sine formula or cosine formula