Trigonometry

Mathematics Worked Examples by Topics

Number	Mathematical Skills	Applications
1	Number, percentages, and percentiles	Determining the amounts, costs, and dimensions of materials
2	Ratio	Scaling models, dimensions, shapes, and drawings
3	Surface area/Volume	Finding costs of quantities, waste amounts
4	Trigonometry	Calculating angles/lengths of products
5	Graphs and charts	Using data to make decisions/visualization of data
6	Coordinates and geometry	Using coordinates for design drawings
7	Statistics	Using data to make informed design decisions

The figure shows a design for a footbridge. Calculate the length of the column. All measurements are in mm.

Step 1) Identify what equation we need to use:

Although hard to see the two lengths and the column make a right angled triangle and so we can use Pythagorus

Step 2) Use pythagorus to work out the column length squared

Column length² = 2675² + 2024² = 11,252,201mm

Step 3) Calculate column length:

Column length = √ 11,252,201 = 3354.4mm

From the footbridge question above. Calculate the angle the column makes with the ground.

Step 1) Identify what trigonometric identity we need to use:

As we have the length opposite, and length adjacent to the angle we are interested in, we will use TAN.

Step 2) Find tan(x) where x is the angle

tan(x) = ^Opposite⁄_Adjacent = ²⁶⁷⁵⁄₂₀₂₄ = 1.3216...

Step 3) Find the angle, x

Angle, x, = tan^-1(1.3216...) = 52.9^o

Trigonometry Questions