The whole solve
A tank stands on flat ground. You stand 30 m from its foot. Its top reads 60°. Find its height.
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- Read: a tank on flat ground.
- Draw: a horizontal leaves the eye.
- Name: height and walk.
- Pick and divide: 60° gives 30√3 m.
- Check: the three sides fit.
Six steps
Read the scene. Draw a horizontal from the eye. Name the two sides. Pick the ratio. Divide. Check with Pythagoras.
Name: call each side opposite, adjacent or hypotenuse. Divide: write the ratio as a division. Then solve for your side.
Rule: Read, draw, name, pick, divide, check.
One tank, worked in full
The walk is 30 m. The height is opposite the angle. The walk is adjacent. So tan 60° = height ÷ 30. Multiply both sides by 30: height = 30 × √3 = 30√3 m.
The line of sight is the hypotenuse. Cos 60° = walk ÷ line of sight. So the line of sight is 30 ÷ cos 60° = 60 m. Here cos 60° = 1/2, and 30 ÷ 1/2 = 60.
Now check: 30² + (30√3)² = 3600 = 60². The three sides fit a right triangle.
| Step | It stops you from |
|---|---|
| Draw | Measuring an angle from the tank wall |
| Name | Choosing a ratio before naming the sides |
| Divide | Writing a rounded decimal when an exact value exists |
| Check | Handing in an answer no one has tested |