Right-Angled Trigonometry Flashcards

All 7 cards in this deck

What is Pythagoras' theorem?

$a^2 + b^2 = c^2$, where $c$ is the hypotenuse (the side opposite the right angle).

Which Pythagorean triples should you recognise?

3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25 — and any multiple of these.
e.g. 6, 8, 10 and 10, 24, 26

What are the steps to find a missing side in a right-angled triangle using trigonometry?

e.g. find the side opposite a 30° angle when the hypotenuse is 12 cm

1. Label the sides O, A, H relative to the given angle: O = $x$, H = 12.
2. Choose the ratio (SOH CAH TOA): $\sin 30° = \frac{x}{12}$.
3. Rearrange and solve: $x = 12 \sin 30° = 6$ cm.

What are the steps to find a missing angle in a right-angled triangle using trigonometry?

e.g. opposite = 5 cm, hypotenuse = 10 cm

1. Label the sides: O = 5, H = 10.
2. Choose the ratio: $\sin \theta = \frac{5}{10}$.
3. Use the inverse function: $\theta = \sin^{-1}(0.5) = 30°$.

What are the side ratios of a 30°, 60°, 90° triangle?

$1 : \sqrt{3} : 2$ — the side opposite 30° is 1, opposite 60° is $\sqrt{3}$, and the hypotenuse is 2.

What are the side ratios of a 45°, 45°, 90° triangle?

$1 : 1 : \sqrt{2}$ — the two equal sides are opposite the 45° angles and the hypotenuse is $\sqrt{2}$ times a shorter side.

What are the steps to find the length of a chord from the radius and the perpendicular distance of the chord from the centre?

e.g. radius 5 cm, chord 3 cm from the centre

1. The perpendicular from the centre bisects the chord, giving a right-angled triangle with hypotenuse 5 and one side 3.
2. Pythagoras for half the chord: $\sqrt{5^2 - 3^2} = 4$.
3. Double it: chord $= 8$ cm.