Laws of Sines and Cosines Formulas o Law
- Slides: 7
Laws of Sines and Cosines
Formulas o Law of sines o Law of cosines or o Heron’s formula or a, b, and c are the lengths of the sides of the triangle P is the perimeter of the triangle A is the area of a triangle
Use the Law of Cosines to find the value of the side x. x Now we plug into the law of cosine formula to find x. Since length is positive, x is approximately 28. 88104097
Two ships leave a harbor at the same time, traveling on courses that have an angle of 140 degrees between them. If the first ship travels at 26 miles per hour and the second ship travels at 34 miles per hour, how far apart are the two ships after 3 hours? For this problem, the first thing that we should do is draw a picture. Once we have the picture, we may be able to see which formula we can use to solve the problem. continued on next slide
Two ships leave a harbor at the same time, traveling on courses that have an angle of 140 degrees between them. If the first ship travels at 26 miles per hour and the second ship travels at 34 miles per hour, how far apart are the two ships after 3 hours? harbor 26 mph*3 hr = 78 miles ship 1 140° x 34 mph*3 hr = 102 miles ship 2 Looking at the labeled picture above, we can see that the have the lengths of two sides and the measure of the angle between them. We are looking for the length of the third side of the triangle. In order to find this, we will need the law of cosines. x will be side a. Sides b and c will be 78 and 102. Angle α will be 140°. continued on next slide
Two ships leave a harbor at the same time, traveling on courses that have an angle of 140 degrees between them. If the first ship travels at 26 miles per hour and the second ship travels at 34 miles per hour, how far apart are the two ships after 3 hours? harbor 26 mph*3 hr = 78 miles ship 1 140° x 34 mph*3 hr = 102 miles ship 2 Since distance is positive, the ships are approximately 169. 3437309 miles apart after 3 hours.
Approximating the area of a triangle Heron’s Formula where P is the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle. OR The area of a triangle equals one-half the product of the lengths of any two sides and the sine of the angle between them. i. e. 1/2 ab sinγ = A
