Unit 3 - Day 6

Day 6

Daily Objective:

Non Right Angle Triangle Trig: Law of Sines, Area of a Triangle.

The Law of Sines is a mathematical formula used to find the angles and side lengths of triangles that don't have a right angle in them. However you still need 1 side length and all three angles. You can use this formula to find the sides of any triangle as long as you know the angles.

Figure 1

Quiz

1. We'll be using Figure 1 for all three questions today. For this first problem the top angle is 50 degrees, the left one is 70 degrees, and the right one is 60 degrees. The bottom of the triangle is 20 feet. How long is the left side?

2. Now the triangle is slightly different. The left corner is 30 degrees, the right corner is 57 and the top angle is 93 degrees. The right side is 4 feet and the left side 5 feet. How long is the bottom? 

3. A triangle has a bottom of 10 feet. The left angle is 48 degrees and the right angle is 12 degrees. How long is the left side.

Answers

1. To solve this problem you need to set it up like this: sine50/20 x sine60/x. Then you must cross multiply the 20 and the sine60. After you have done this you then divide by sine50 to get a final answer of 22.61 feet.

2. You can set up this problem 2 ways but I am going to do it with the right side. Set up the problem like sine30/4 x sine93/x. Cross multiply the 4 and sine93 and then divide by sine30 to get a final answer of 7.9 feet.

3. First find the last angle which is 120 degrees. Then set up the problem like sine120/10 x sine12/x. Then cross multiply the 10 and sine12 and then divide by sine120 to get a final answer of 2.4 feet.