Question

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

Accepted Answer

Identify the type of triangle problem you are dealing with: whether it is a right triangle or an oblique triangle (non-right). This will determine which trigonometric methods to use. List the given information from the problem: known sides and angles. This is essential to decide which formulas or laws to apply. If the triangle is right-angled, use basic trigonometric ratios (sine, cosine, tangent) to find missing sides or angles. For example, use $$\sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}}$$, $$\cos 	heta = \frac{	ext{adjacent}}{	ext{hypotenuse}}$$, or $$	an 	heta = \frac{	ext{opposite}}{	ext{adjacent}}. If $$the triangle is oblique, apply the Law of Sines or Law of Cosines depending on the known elements: 
- Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
- $$Law of Cosines: $$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$ \cos C$$ (and similarly for other sides). After calculating the missing sides and angles, round the side lengths to the nearest tenth and the angle measures to the nearest degree as instructed.

In Exercises 1–8, solve each triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree.

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Key Concepts

Types of Triangles and Their Properties

Law of Sines and Law of Cosines

Rounding and Angle Measurement