Law of Sines and Law of Cosines — a Deeper Look Answers

Just as you saw Triangle A B D used to create an equation for c2, use Triangle C B D to create an equation for a2. Solve this equation for h2. ✔ h2 = a2 - x2X h2 = a2 + x2x2 = a2 + h2

Replace your expression for h2 in c2=h2+b2-2bx+x2.✔ C2 = a2 - x2 + b2 - 2bx + x2c2 = a2 + x2 + b2 - 2bx + x2X c2 = -a2 - x2 + b2 - 2bx + x2

If all of the side lengths of a triangle had a length of 1, what would the simplified law of sines equation be?

Which of the following did you do? Check all of the boxes that apply.

After starting with a non-right triangle, you had to construct the base✔ altitudebisectorhypotenuse.

After forming two right triangles, which right triangle theorem did you have to use twice to solve for side lengths that were not in the final equation?

Two trains leave a station on different tracks. The tracks make an angle of 115° with the station as a vertex. The first train travels 200 kilometers and makes its first stop in Pocomoc, while the second train travels 350 kilometers and makes it first stop in Easton. How far apart are the trains when both are at their first stop? Round the answer to the nearest tenth.

Use right triangle CDB to create a trigonometric ratio for sin C.

What type of triangles did you have to construct to start the proof?

There are two cables coming off the top of a building from the same point. Each cable is secured to the ground. The longest cable is 200 ft. It is attached at point M and creates a 32° angle of elevation with the ground. The other cable is attached at point N. If the angle formed between the two cables at the top of the building is 25°, what is the distance between points M and N?Measure of Ð N = °

After solving the two sine equations for h, you get .

What does the common side length (h) in each of the sine equations represent in ?ABC?

x = ft