Right-angled trigonometry · Year 11

In Year 11 you learn: angles of elevation and depression.

Trigonometry links the angles and sides of right-angled triangles. Label the sides from the angle you are using (opposite, adjacent, hypotenuse), choose sin, cos or tan with SOH CAH TOA, and you can find any missing side or angle.

Key facts

  • Hypotenuse: the longest side, opposite the right angle. Opposite: across from θ. Adjacent: next to θ.
  • SOH: sin θ = opposite ÷ hypotenuse.
  • CAH: cos θ = adjacent ÷ hypotenuse.
  • TOA: tan θ = opposite ÷ adjacent.
  • To find an angle, use the inverse: θ = sin⁻¹(…), cos⁻¹(…) or tan⁻¹(…).
  • Angles of elevation (looking up) and depression (looking down) are measured from the horizontal.

Worked examples

Example 1

Find x, to 1 d.p.

Answer: x = 12.6 cm

Example 2

A ramp rises 1.2 m over a sloping length of 8 m. What angle does it make with the ground, to 1 d.p.?

Answer: 8.6°

Example 3

From the top of a 40 m cliff, the angle of depression to a boat is 22°. How far is the boat from the foot of the cliff, to the nearest metre?

Answer: 99 m

Other years