Pythagoras in two and three dimensions, SOHCAHTOA for sides and angles, the exact trig values you must memorise, and the sine and cosine rules.
You can study this deck without signing up — your progress is kept in this browser. An account saves it properly, syncs it across devices, and lets you edit the cards.
1.State Pythagoras theorem.
a squared + b squared = c squared, where c is the hypotenuse.
2.Which side is the hypotenuse?
The longest side, always opposite the right angle.
3.When can Pythagoras be used?
Only in a right angled triangle, and only when you know two sides and want the third.
4.Find the hypotenuse of a triangle with sides 3 and 4.
9 + 16 = 25, so the hypotenuse is the square root of 25 = 5.
5.How do you find a shorter side using Pythagoras?
Subtract instead of add: c squared minus the known side squared, then take the square root.
6.The hypotenuse is 13 and one side is 5. Find the other side.
169 minus 25 = 144, so the side is 12.
7.What does SOHCAHTOA stand for?
Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent.
8.Which side is the opposite?
The side directly across from the angle you are using.
9.Which side is the adjacent?
The side next to the angle that is not the hypotenuse.
10.How do you find an angle using trigonometry?
Work out the ratio of the two known sides, then use the inverse function such as inverse sine.
11.When do you use tan?
When the two sides involved are the opposite and the adjacent.
12.What is sin 0?
0
13.What is sin 30?
One half.
14.What is sin 90?
1
15.What is cos 0?
1
16.What is cos 60?
One half.
17.What is tan 45?
1
18.What is sin 45 and cos 45?
Both equal 1 over the square root of 2, which is the same as the square root of 2 over 2.
19.State the sine rule.
a divided by sin A = b divided by sin B = c divided by sin C.
20.When do you use the sine rule?
When you have a matching pair of a side and its opposite angle, in a non right angled triangle.
21.State the cosine rule.
a squared = b squared + c squared minus 2bc cos A.
22.When do you use the cosine rule?
When you know three sides, or two sides and the angle between them.
23.State the formula for the area of any triangle using trigonometry.
area = one half x a x b x sin C, where C is the angle between sides a and b.
24.How do you apply Pythagoras in three dimensions?
Use it twice: once to find a diagonal across the base, then again with the height to find the full diagonal.
25.What is an angle of elevation?
The angle measured upwards from the horizontal to a line of sight.
26.What is an angle of depression?
The angle measured downwards from the horizontal to a line of sight.
You remember far more by trying to recall an answer than by reading it. Run these as flashcards and the ones you keep getting wrong will come back more often.
Start studyingOr see the other Geometry and Measures decks.