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

Which equation below is a true statement about ?

To start the proof of the Law of Cosines, an altitude is constructed. Which of the following is formed due to the construction of the altitude in a non-right triangle?

What is the length of side q, given r = 20, s = 30, and Q = 15°? Round the answer to the nearest tenth. [Not drawn to scale]

Which equation represents the Law of Sines for ?

The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle measure are given. [Not drawn to scale]What is the measure of angle X? Round the answer to the nearest tenth.

Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth. [Not drawn to scale]

Which equation below is a true statement about ?

Eddie solved for the length of side c in using the Law of Cosines formula, . Sophia wants to solve for the side length of b. Which equation could Sophia use to solve for the side length of b, given the other two side lengths and the measure of their included angle?

In below, and . Which of the following combines the two sine ratios into one equation?

In the proof of the Law of Cosines, the equation was created using the Pythagorean theorem. Which equation is a result of expanding ?