This example is very similar to the last one, the values are very familiar. The idea is to try and become more fluent with the rules and understand which needs to be used and where. Try and stay one step ahead of me in your head as you move through the problem.
Q: Calculate the length of the hypotenuse based on the picture below.
1) Identify the right angle in your triangle. This confirms that you will be able to use the sohcahtoa rule.
2) Identify your angle of interest. This will change which sides are opposite and adjacent.
Circled in red is the angle of interest. With this in hand we can now identify the legs of the triangle.
3) Identify your opposite and adjacent legs of the triangle.
The closest side is the adjacent side, labelled in pink, and the furthest side is the opposite, labelled in blue.
4) Using the sohcahtoa rule, set up a relationship using sin/cos/tan, the angle, and two of the adjacent/opposite/hypotenuse sides.
In this problem, the three critical components are the angle theta, the adjacent side and the hypotenuse. This means that cosine, e.g. cah of sohcahtoa, will be the key to solving the problem. It includes all 3 of the components we have in the problem.
5) Solve the equation for your desired variable.
Unlike last problem, we're calculating the cosine of an angle, remember to check if you're in radians or degrees mode!
6) Box your answer, you're done!
So with this, we solve for our hypotenuse of length 5. Very little surprise there. But it means that we were on the right track and are sure of our answer. How did you do? Was this problem quicker than the last? Do you feel more confident with the steps? Have you gained fluency? If the answer to any of those is yes you are certainly on the right track.
