4.4 Trigonometry

• Angles and sides of right-angled triangles
• Trigonometric ratios for acute angles

• identify angles and sides of right-angled triangles in different situations
• identify sine, cosine and tangent ratios from a right-angled triangle in different situations
• read tables of trigonometric ratios for acute angles
• determine trigonometric ratios of acute angles using calculators
• apply trigonometric ratios to calculate lengths and angles of right-angled triangles in different situations
• appreciate the use of trigonometric ratios in real-life situations

“What is the relationship between angles and sides in a right-angled triangle?”

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1. Naming the sides of a right-angled triangle
   40 min · 1 practice tasks · quiz
   Hypotenuse, opposite and adjacent, named from whichever acute angle you have marked.
2. Sine, cosine and tangent
   40 min · 1 practice tasks · quiz
   Three ratios, one for each way of pairing two sides of a right-angled triangle.
3. Tables and calculators
   40 min · 1 practice tasks · quiz
   The value of a ratio for a given angle comes from a table of figures or from a calculator.
4. Finding a length: the unknown on top
   40 min · 1 practice tasks · quiz
   Choose the ratio from the two sides involved, write the equation, and multiply.
5. Finding a length: the unknown underneath
   40 min · 1 practice tasks · quiz
   When the unknown sits on the bottom of the fraction, it swaps places with the ratio.
6. Finding an angle
   40 min · 1 practice tasks · quiz
   Work out the ratio from two sides, then use the inverse key to turn it back into an angle.
7. Trigonometry in real situations
   40 min · 1 practice tasks · quiz
   Ladders, ramps and the heights of trees, answered faster than by scale drawing.