This week in math we learned how to use and apply the sine law. This understanding is important because in combonation with the cosine law, you can tackle any triangle no matter what type. This understanding is also apart of the foundation of our math skills for the future, and is extremely useful. I chose this topic because I find that it is a simple way to deal with complicated looking triangles.
Lets take a look at some examples.
Example 1.
Step 1. Refering to the sine law which has been written at the top of the paper, appy the appropirate sine law to use in order to determine the length of b. Once you have determined which sine law you are to use, plug in your values to the formula.
Step 2. After plugging in your values, we can cross multiply to help solve this equation and get rid of the fractions.
Step 3. Since we are looking for side b, we want to isolate it. I divide both sides of the equation by sine 80 degrees to isolate b.
Step 4. Finally we can plug this all into our calculator to get our value for b. Remeber, round to the nearest tenth of a cm.
Example 2.
(In this example the shape/sketch of the triangle is given to us already)
Step 1. Apply the appropriate sine law: We are looking for angle J and we have all the info for sine H so we use these two. After determining your sine law, plug in your values to the formula.
Step 2. Cross multiply to get rid of fractions.
Step 3. Since we are looking for angle J, we want to isolate. I divide both sides of the equation by 7 to do so.
Step 4. Calculate : my answer is 80 degrees, however, since the diagram was given to use it shows that angle J is much wider than 80 degrees, so we can reject this solution. Being a detective, we know that questions with sine law can have two answers. In quadrant one and in quadrant two.
Step 5. Lets use our understandings to calculate angle J in quadrant two. 180-80 gives us 100 degrees.
Glossary :
Sine Law : the ratio of side length to the sine of the opposite angle