Question

Solve the triangle ABC with a=123,b=224,c=28minutes and 40 seconds?

Answer 1

`color(blue)("side " c = 101),color(red)( "Area of triangle " A_t = 114.21 " sq units"`

Explanation:

`"Given : " a = 123, b = 224, hatC = 28' 30 sec`

First let's convert `hatC` into degrees.

60" = 1' , `60' = 1^@`, 3600" = `1@`

`:. 0^@ 28' 30`" = `0 + 28/60 + 30/3600 = 0.475^@`

Area of triangle `A_t = (1/2) a b sin C`

`A_t = (1/2) * 123 * 224 * sin (0.475^@) = color(red)(114.21 " sq units"`

Third side c can be obtained by using Law of Cosines

`c^2 = a^2 + b^2 - 2 a b cos C`

`c^2 = 123^2 + 224^2 - 2 * 123 * 224 * cos (0.475^@)`

`c^2 = 10202.89`

`color(blue)("side " c = 101 " units"`