Year 10 - Trig Ratio Calculation

Ratio first. Calculator second.

This lesson slows the work down: identify the useful pair of sides, pick sin, cos or tan, choose the correct line of working, then calculate.

20write sin, cos or tan

20find missing side x

20find angle x

SOHsin uses opposite and hypotenuse

CAHcos uses adjacent and hypotenuse

TOAtan uses opposite and adjacent

The order

1find the marked angle

2name the two useful sides

3match SOH, CAH or TOA

4calculate x

The unused side is ignored. The marked angle controls opposite and adjacent.

Refresher

Choose the ratio from the two sides

Do not start with the calculator. Start by naming the pair of sides involved.

Side pairs

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

What to write

For these first questions, type exactly one ratio into the box: sin, cos, or tan.

Example: if the useful sides are opposite and hypotenuse, write sin.

Missing side

Choose the line of working, then calculate x

The multiple choice answers show possible working. Choose the correct setup first, then use a calculator for the actual number.

x on top

sin(35) = x / 12

Multiply: x = 12 * sin(35)

x on bottom

cos(52) = 7 / x

Divide: x = 7 / cos(52)

Missing angle

Use inverse trig to find angle x

When the angle is missing, the ratio is still chosen from the two given sides. The last step uses inverse sin, inverse cos, or inverse tan.

Example

tan(x) = 9 / 14

x = tan^-1(9 / 14)

Calculator answer

After the correct working is chosen, calculate the angle and enter it rounded to 1 decimal place.

Make sure the calculator is in degrees.

Section Question

Question

Question 1 of 60

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Complete

Trig ratio calculation summary

The key skill is the chain: side pair, ratio, working, calculator answer.

0 / 20ratio writing

0 / 20missing side

0 / 20missing angle