Mathematics·Bearings and trigonometry · NSSCO 11.1
Pythagoras & trigonometric ratios
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Right-angled triangles hide a superpower: from just a few facts you can find every missing side and every missing angle. In this lesson we name the three sides, master Pythagoras' theorem for finding any side, meet the three trigonometric ratios (SOH-CAH-TOA), find unknown sides and unknown angles, and then point it all at real life — the height of a flagpole, the slope of a ramp, the angle of a ladder, and the distance to a boat seen from a cliff.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 11.1):
- Recall and use Pythagoras' theorem to find any side of a right-angled triangle
- Name the hypotenuse, opposite and adjacent sides relative to a chosen angle
- Use the sine, cosine and tangent ratios (SOH-CAH-TOA) for acute angles
- Find an unknown side of a right-angled triangle using a trigonometric ratio
- Find an unknown angle using the inverse ratios sin⁻¹, cos⁻¹ and tan⁻¹
- Solve two-dimensional problems involving angles of elevation and depression
- Apply Pythagoras and trigonometry to real problems such as ladders, ramps and heights
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