Question
$$\begin{aligned}&\text {Solve each triangle}\text { if the triangle has a solution. Use decimal degrees for angle measure.}\end{aligned}$$$a=10.5$ miles, $b=20.7$ miles, $c=12.2$ miles
Step 1
The law of cosines states that $c^2 = a^2 + b^2 - 2ab\cos(C)$. Rearranging for $\cos(C)$ gives us $\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$. Substituting the given values, we get: \[\cos(\alpha) = \frac{b^2 + c^2 - a^2}{2bc} = \frac{(20.7)^2 + (12.2)^2 - (10.5)^2}{2 Show more…
Show all steps
Your feedback will help us improve your experience
Ahmad Reda and 64 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
$$\begin{aligned} &\text {Solve each triangle}\text { if the triangle has a solution. Use decimal degrees for angle measure.} \end{aligned}$$ $a=6.00$ kilometers, $b=5.30$ kilometers, $c=5.52$ kilometers
Additional Topics in Trigonometry
Law of Cosines
Solve each triangle using the law of cosines. $$\begin{aligned} \text { side } c &=25.8 \mathrm{mi} \\ \angle B &=30^{\circ} \\ \text { side } a &=12.9 \mathrm{mi} \end{aligned}$$
Applications of Trigonometry
The Law of cosines; the Area of a Triangle
Solve each triangle. $C=59.70^{\circ}, a=3.725$ miles, $b=4.698$ miles
Applications of Trigonometry and Vectors
The Law of Cosines and Area Formulas
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD