Question

Can someone please help me

-Solve each triangle. Round to the nearest tenth, if necessary.

show work

Answer 1

• T = 20°
• t = 29.0
• u = 17.7

Explanation:

You want the solution to triangle TUV, given U=12°, V=148°, v=45.

Triangle solution

Solving a triangle generally means finding the measures of all sides and angles. When two angles and one side are given, and that side is opposite the largest angle, there is one solution. It can be found using the Law of Sines.

Missing angle

The Angle Sum theorem tells you the sum of angles in a triangle is 180°. This means ...

T +U +V = 180°

T +12° +148° = 180°

T = 20° . . . . . . . . . . . . subtract 160°

Missing Sides

The Law of Sines tells you the side lengths are proportional to the sine of the opposite angle:

t/sin(T) = u/sin(U) = v/sin(V)

t = v/sin(V)·sin(T) = 45/sin(148°)·sin(20°) ≈ 29.0 . . . . multiply by sin(T)

u = v/sin(V)·sin(U) = 45/sin(148°)·sin(12°) ≈ 17.7 . . . . . multiply by sin(U)

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Additional comment

There may be two solutions if the given side is not opposite the largest angle.