Due to the surge in COVID-19 cases in the district, week 16 was canceled. On week 17, we finished off the remaining lessons on Trigonometry.

The Sine Law is defined as the ratios of the SINE of an angle to the length of its opposite side are equal. This law is used on acute or obtuse triangles in order to determine the length of a side when the measures of 2 angles and the length of 1 side are given. It also determines the measure of an angle when the lengths of 2 sides and the measure of an angle are given.

For any ∆ABC,

Let’s use this Law on one of the review questions: In ∆ABC, c=10cm,∠C=52°, and ∠B=60°, determine the value of b.

For the Cosine Law, the Pythagorean Theorem is utilized in order to determine a length of a side when the lengths of 2 sides and the measure of a contained angle are known, or the measure of any angle of a triangle when all 3 sides of that triangle are known.
For any ∆ABC,

We will use this Law on another review question: In ∆ABC, c=10cm,b=9cm,a=8cm, determine the value of ∠C.

Several tricky word problem exercises gave only measures of angles and/ or sides and asked to solve other angles or sides without mentioning which Law to use. Here’s a good example (question#7 on page 517):
A cross-country runner runs due east for 6km then changes course to E25°N and runs another 9km. How far is the runner from her starting point?

Because of the change of course, E25°N becomes 155° inside the triangle created.
(180°-25°=155°)
With the known values of only 2 sides and 1 angle, COSINE LAW is the best solution to solve the distance (third side).

The runner was 14.7 km from her starting point.