Choosing the Ratio

Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 10 of 50.

Three ratios, one memory word: SOH CAH TOA. Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.

To choose, name two sides: the one you know and the one you want, both read from the same angle. Then pick the ratio that holds exactly those two. A ladder 9 m long makes 40° with the ground and you want how far its foot is from the wall: that side is adjacent to 40° and the ladder is the hypotenuse, so the cosine links them.

The board checks your choice. Tap 40°, the foot and the ladder and pick Sine ratio, and it writes nothing: it says the rule does not link those parts and waits for another pick. It also knows the exact ratios of 30°, 45° and 60°, so it can work out tan 60° for you: it is √3. Chapter 6 shows where these values come from.

Challenge

Triangle ABC has a right angle at C and a 60° angle at A. The side next to the 60° angle is 5. Find the side x opposite the 60° angle. Choose the ratio yourself, and leave the answer exact. Then press Check.

Try it yourself

$Use the figure to find x$