Which side is the hypotenuse?

The longest side, opposite the right angle.

How do you find an unknown angle?

Use the inverse function, e.g. \theta=\sin^{-1}(\ldots).

Opposite 7, adjacent 9: find \theta.

\tan^{-1}\left(\frac79\right)=37.9^\circ

What is the angle of elevation?

The angle upwards from the horizontal to the line of sight.

What is the angle of depression?

The angle downwards from the horizontal to the line of sight.

Unknown side in the denominator, e.g. \tan25^\circ=\frac{60}{d}?

Divide: d=\frac{60}{\tan25^\circ}.

Trigonometric ratios in right-angled trianglesIB MYP Maths Standard: Flashcards

Card 1 of 140 of 14 known

Question

What is $\sin\theta$ in a right-angled triangle?

Tap or press Space to reveal

Tap card or press Space to flip

See all 14 cards

What is $\sin\theta$ in a right-angled triangle?: $\frac{\text{opposite}}{\text{hypotenuse}}$
What is $\cos\theta$ ?: $\frac{\text{adjacent}}{\text{hypotenuse}}$
What is $\tan\theta$ ?: $\frac{\text{opposite}}{\text{adjacent}}$
Memory aid for the three ratios?: SOH CAH TOA
Which side is the hypotenuse?: The longest side, opposite the right angle.
How do you find an unknown angle?: Use the inverse function, e.g. $\theta=\sin^{-1}(\ldots)$ .
Hyp $10$ , angle $30^\circ$ : find the opposite side.: $10\sin30^\circ=5$
Opposite $7$ , adjacent $9$ : find $\theta$ .: $\tan^{-1}\left(\frac79\right)=37.9^\circ$
What is the angle of elevation?: The angle upwards from the horizontal to the line of sight.
What is the angle of depression?: The angle downwards from the horizontal to the line of sight.
How are elevation and depression for the same line related?: Equal (alternate angles).
Unknown side in the denominator, e.g. $\tan25^\circ=\frac{60}{d}$ ?: Divide: $d=\frac{60}{\tan25^\circ}$ .
What mode should the calculator be in?: Degrees.
Other acute angle if one is $37.9^\circ$ ?: $90^\circ-37.9^\circ=52.1^\circ$

Exam questions on Trigonometric ratios in right-angled triangles

A ladder $5$ m long rests against a vertical wall on level ground. The foot of the ladder is $1.5$ m from the wall.
The foot of the ladder is moved so that it is $2$ m from the wall. Find the new angle between the ladder and the ground.2 marks
A hiker stands at the top of a vertical cliff that is $60$ m above the sea. She looks at a boat on the sea and measures the angle of depression of the boat as $25^\circ$ .
The boat sails $40$ m straight towards the cliff. Find the new angle of depression of the boat, to $1$ decimal place.2 marks
In triangle $ABC$ , angle $B=90^\circ$ , $AB=7.2$ cm and $AC=11.5$ cm.
Find the size of angle $BAC$ , to $1$ decimal place.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).