Question

2.

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Answer 1

Following are the responses to the given question:

Explanation:

`\angle C= 180 - ( 26 + 51 )\\\\C = 103^(\circ)`

applying the law of sines to find the unknown sides:

`\to (a)/(\sin A) = (c)/(\sin C)\\\\\to (a)/(\sin 26) = (28)/(\sin 103)\\\\a=(28 * \sin 26 )/(\sin 103)\\\\a=(28 * 0.438371147 )/(0.974370065)\\\\a=(12.2743921 )/(0.974370065)\\\\a=12.597259\\\\a=12.59\\\\a = 12.6 \ m\\\\`

`\to (b)/(\sin 51) = (28)/(\sin 103)\\\\\to b=(28 * \sin 51 )/(\sin 103)\\\\b=(28 * 0.777145961 )/(0.974370065)\\\\b=(21.7600869 )/(0.974370065)\\\\b=22.3324681\\\\b=22.3\\\\b = 22.3 \ m\\\\`

so,

`\angle C = 103^(\circ)\\\\\to AC = 22.3\ m\\\\\\to BC = 12.6 \ m`