1.A ladder leans up against a building at an angle of 65° with the ground. If the ladder is 5 metres long, how far up the building does it reach?
2.A student is overheard saying: "I don't need to learn the Primary Trig Ratios. I am just going to use the Sine and Cosine Laws to solve problems." Show by example that the student is right. Explain the advantages and disadvantages to this approach.
(a) Now write down the Sine Rule (Law), and simplify it using the fact that . Using this simplified equation, write down expressions for and .
(b) Write down the Cosine Rule (Law) that begins , and simplify it using the fact that . What well-known formula does this give you?
Can you see why the student is right in saying he doesn't need to learn the Primary Trig Ratios?
(c) One advantage of this method is that there aren't so many rules to learn. Can you think of a disadvantage?