Which quotient, which side

Every problem starts with one choice. Which ratio do I use?

Name two sides first

Pick the ratio that joins your known side and your wanted side.

At the angle of elevation, the height is the opposite side. The walk is the adjacent side. The line of sight is the hypotenuse.

Each ratio joins two sides.

Rule: Name the side you know and the side you want. That pair picks sin, cos or tan.

Three examples

A kite string is 60 m long. The string makes 30° with the ground. You know the string and want the height. So use sin. Sin 30° = 1/2. Height = 60 × 1/2 = 30 m.

Now you know the string and want the distance along the ground. So use cos. Cos 30° = √3/2. Distance = 60 × √3/2 = 30√3 m.

A tower is 30 m tall and you stand 30 m away. No angle is given. Use Pythagoras: height² + walk² = line of sight². So line of sight² = 30² + 30² = 1800. Then the line of sight is √1800 = 30√2 m. This works because 1800 = 900 × 2 and √900 = 30.

Try the lab to finish this lesson.