Mathematics Topic
Trigonometry: Finding Missing Sides
- Read notes
- Flashcards
- Quiz
- Confident
Study focus - 3 things
- Trigonometry connects angles and side lengths in right-angled triangles
- Use SOH-CAH-TOA to choose sine, cosine, or tangent
- Label opposite, adjacent, and hypotenuse before calculating
Section 1Right-angled triangles
Grade 9 trigonometry works with right-angled triangles. The hypotenuse is always the longest side and is opposite the right angle. Watch out: the opposite and adjacent sides depend on the angle you are using.
Section 2SOH-CAH-TOA
SOH-CAH-TOA helps you choose the ratio. Sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, and tangent = opposite / adjacent. Here's the trick: label first, choose ratio second.
Section 3Finding sides
To find a missing side, choose the trig ratio that uses the given angle, given side, and missing side. Substitute the values and rearrange. Keep enough decimal places while working, then round at the end.
Section 4Calculator mode
Most school trigonometry angle questions use degrees. Check that the calculator is in degree mode before using sin, cos, or tan. If the answer looks wild, degree mode is one of the first things to check.
Examples
A right triangle has angle 30 degrees and hypotenuse 10 cm. Find the opposite side.
Use sine because opposite and hypotenuse are involved. sin 30 = opposite / 10, so opposite = 10 x sin 30 = 5 cm.
A ladder leans against a wall in Kingston. The ladder is 6 m long and makes a 60 degree angle with the ground. Find the height up the wall.
The height is opposite the 60 degree angle and the ladder is the hypotenuse. sin 60 = height / 6, so height = 6 x sin 60 = about 5.20 m.
Now let's water it
Session runs notes to flashcards to quiz back-to-back.