Right triangle
In a right triangle, the sides and angles are connected. If you know two of them (at least one side), you can work out the rest with sine, cosine and tangent.
The explanation is shown. Quick: the three common combinations. Advanced: all six, sin/cos/tan, area and what happens when the angle or the side changes.
Your numbers
Answer
a
2.8
b
4
c
4.88
Angle A
35°
Angle B
55°
Angle C
90°
How to work it out
- 1a = b · tan A = 4 · tan 35° = 2.8
- 2c = b / cos A = 4 / cos 35° = 4.88
- 3B = 90° − A = 90° − 35° = 55°
The formula
sin A = a / c
The opposite leg divided by the hypotenuse.
cos A = b / c
The adjacent leg divided by the hypotenuse.
tan A = a / b
The opposite leg divided by the adjacent leg.
A + B = 90°
The two acute angles in a right triangle always add up to 90°.
In depth: more numbers and “what if”
More quantities
| Size | Value |
|---|---|
| sin A = a / c | 0.5736 |
| cos A = b / c | 0.8192 |
| tan A = a / b | 0.7002 |
| Area (a · b / 2) | 5.6 |
| Perimeter (a + b + c) | 11.68 |
| Height to the hypotenuse (a · b / c) | 2.29 |
What if angle A is different?
| Angle A | a | b | c |
|---|---|---|---|
| 25° | 1.87 | 4 | 4.41 |
| 30° | 2.31 | 4 | 4.62 |
| 35° | 2.8 | 4 | 4.88 |
| 40° | 3.36 | 4 | 5.22 |
| 45° | 4 | 4 | 5.66 |
More: Geometry
- PythagorasFind the missing side, set out a right angle, check whether a room is square, and find the space diagonal.
- Area and perimeterRectangle, triangle, trapezium, circle and composite shapes — area and perimeter.
- Volume and surface areaBox, cylinder, cone, sphere, pyramid, prism, pipe and frustum — also in litres.
- The circleRadius, circumference and area from one measurement — plus sector, annulus, chord and rise.
- AnglesThe third angle in a triangle and the angle sum of a polygon.
- Points in the coordinate systemDistance, midpoint and the line between two points — drawn in.
- Similar figuresScale factor and missing sides — area is multiplied by k², volume by k³.
- Any triangleThe sine and cosine rules: find the rest from SSS, SAS, ASA or SSA.
- TransformationsReflect, rotate and translate a figure on a coordinate grid — before and after.