# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-geometry-trigonometry-3d%20geometry.html


## Trigonometry -3D Geometry

" Even at midnight, the city groans in the heat. We have had no rain for quite a while. The traffic sounds below ride the night air in waves of trigonometry, the cosine of a siren, the tangent of a sigh, a system, an axis, a logic to this chaos, yes. " Lorrie Moore


#### Surface area of complex shapes


##### What you have to know:

- You must be able to manipulate algebraic expressions. (If not, check this lesson)
- You must know the formulas of surface area and volume of 3D shapes. (If not, check this file)

##### Key Points

- 1. Watch the video:

#### Volume of 3D solids


##### What you have to know:

- You must know the formulas of volume for common 3D shapes.

##### Key Points

- 1. Watch the video:

#### 3D Pythagoras


##### What you have to know:

- The basic trigonometric properties (If not, check this lesson)

##### Key Points

- 1. Watch the video:

#### Angles of elevation and depression


##### What you have to know:

- The basic trigonometric properties (If not, check this lesson)

##### Key Points

- 1. Watch the video:

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 5A, 5B, 5C

##### Key Points

- 1. You should be able to find the angle between two intersecting lines in two dimensions.
- 2. You should be able to use the sine rule to find side lengths and angles in non-right-angled triangles: \[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}, \qquad \text{or} \qquad \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}. \]
- 3. You should be able to use the cosine rule to find side lengths and angles in non-right-angled triangles: \[ a^2 = b^2 + c^2 - 2bc\cos A, \qquad \text{or} \qquad \cos A = \frac{b^2 + c^2 - a^2}{2bc}. \]
- 4. You should be able to find the area of a triangle when the perpendicular height is not known: \[ \text{Area} = \tfrac{1}{2}ab\sin C. \]
- 5. You should be able to find the angle between two intersecting lines in three-dimensional shapes, and the angle between a line and a plane in three-dimensional shapes.
- 6. You should be able to construct diagrams from given information, use trigonometry in questions involving bearings, and use trigonometry in questions involving angles of elevation and depression.

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