Common Core · High school
HSG-SRT.C.6
High school — Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle.
High school — Understand that side ratios in right triangles are properties of the angles, leading to definitions of sine, cosine and tangent.
The 2 skills that cover it
- Special Right TrianglesUse the 45-45-90 and 30-60-90 side ratios to find exact side lengths written with radicals, and recognise the two triangles inside squares, equilateral triangles and hexagons.Read the lesson →
- Right Triangle TrigonometryUse sine, cosine and tangent as ratios of sides in a right triangle to find unknown sides and angles.Read the lesson →
What a student should be able to do
- Find the hypotenuse or a leg of a 45-45-90 triangle exactly.
- Find any side of a 30-60-90 triangle from any other side exactly.
- Recognise special right triangles inside squares, equilateral triangles and regular hexagons.
- Solve problems whose answers are exact lengths in simplest radical form.
- Identify the opposite, adjacent and hypotenuse sides for an angle.
- Use SOH-CAH-TOA to find a missing side.
- Use inverse trig functions to find a missing angle.
- Solve angle-of-elevation and depression problems.