GCSE · Pythagoras & right-angled trigonometry

Exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)Exam-style questions

Where the exact values of sin, cos and tan come from: two triangles you can sketch in seconds, half a square and half an equilateral triangle, plus a ladder lying flat or standing upright for 0° and 90°. How to use them to find an exact side in surd form, how to get an angle back from an exact ratio, and how to answer a non-calculator "show that" with exact values.

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20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows a right-angled triangle $ABC$ .Diagram NOT accurately drawn

Angle $ABC = 90°$ and angle $BAC = 30°$ .

The perimeter of the triangle is $12$ cm.

Work out the exact length of $AB$ .

Give your answer in the form $a + b\sqrt{3}$ , where $a$ and $b$ are integers.

(5 marks)
Level 5 · 5 marksTry it
2
The diagram shows a triangular field, $JKL$ .Not to scale

$JK = 50$ m, $JL = 80$ m and angle $KJL = 60°$ .

A straight path goes from $J$ to the side $KL$ .

The path meets $KL$ at right angles.

Work out the exact length of the path.

Give your answer in its simplest form.

You must show your working.

(6 marks)
Level 5 · 6 marksTry it