Right-angled trigonometry GCSE lesson: SOHCAHTOA, sides, angles and exact values

Trigonometry: practice

Label H, O and A on a sketch first. Keep your calculator in degrees. Round only at the end, as each question says. The stretch is without a calculator.

Diagnostic question: choose and explain

1. Triangle ABC has its right angle at B. Angle A is 35° and AB = 8 cm. Which gives the length of BC?
   1. BC = 8 × sin 35°
   2. BC = 8 ÷ tan 35°
   3. BC = 8 × tan 35°
   4. BC = 8 × cos 35°

Practice questions

1. Triangle PQR has its right angle at Q. First the angle θ is at P, then at R. Sort each side into what it is from that angle.They sort 6 items into Hypotenuse and Opposite θ and Adjacent to θ.
2. Which ratio would you use? Sort each question by the two sides it has.They sort 6 items into sin and cos and tan.
3. A right-angled triangle has an angle of 30° and hypotenuse 14 cm. Find the side opposite the 30° angle, in cm.
4. A right-angled triangle has an angle of 52°. The side next to it (not the hypotenuse) is 9 cm. Find the side opposite the 52° angle, in cm to 1 decimal place.
5. The opposite side is 8 cm and sin θ = 0.4. So 8/x = 0.4, where x is the hypotenuse. Solve it line by line.They solve 8/x = 0.4 line by line, each line checked as they write it.
6. A right-angled triangle has hypotenuse 12 cm. The side opposite the angle θ is 7 cm. Find θ in degrees, to 1 decimal place.
7. Sam types sin⁻¹(0.5) into a calculator and gets 0.52. The angle should be 30°. What went wrong?
   1. 0.52 is 30° rounded
   2. The calculator is set to radians, not degrees
   3. Sam should have typed sin(0.5)
8. Without a calculator: mark cos 30° on the number line.They drag a marker on a number line from 0 to 1.
9. A ladder 6 m long leans against a wall and reaches 5.2 m up it. Find the angle between the ladder and the flat ground, to the nearest degree.
10. Stretch, without a calculator: a right-angled triangle has hypotenuse 10 cm and an angle of 60°. The side next to the 60° angle is ___ cm, and the side opposite it is exactly ___ cm. Write the second as a surd: type √ or sqrt, such as 2√5 or 2sqrt5.

Support: For question 1: put your finger on the right angle; the side across from it is the hypotenuse. Put your finger on θ; the side across from it is the opposite. The side left is the adjacent. Then choose: O and H, sin; A and H, cos; O and A, tan.

Trigonometry: exit

Label the triangle first. One sentence for the second part.

1. A right-angled triangle has hypotenuse 15 cm and an angle of 40°. Find the side next to the 40° angle (not the hypotenuse), in cm to 1 decimal place.
2. Without a calculator, write down sin 30°, cos 60° and tan 45°. Then say in one sentence where one of them comes from.

Exit check

A side found and three exact values show who labels and chooses the ratio, and who knows the special angles.

Find a side next to a given angle from the hypotenuse.

Trigonometry: sides, angles and exact values

Sketch each triangle and label H, O and A from the angle before you choose a ratio. Keep your calculator in degrees. Questions 1 and 6 are without a calculator.