Edexcel GCSE Maths: Trigonometry Worked Solutions

Question

Here is triangle ABC with AB = 5 cm, BC = 10 cm, and AC = 5√7 cm. Find the size of angle ABC. You must show all your working.

Worked Solution

1. 1

   Use the cosine rule to find angle B. The cosine rule states: AC² = AB² + BC² – 2 · AB · BC · cos B.

2. 2

   Substitute the known values: (5√7)² = 5² + 10² – 2(5)(10) cos B. Calculate each term: (5√7)² = 175, 5² = 25, 10² = 100. So 175 = 125 – 100 cos B.

3. 3

   Rearrange: 100 cos B = 125 – 175 = –50, so cos B = –50/100 = –1/2.

4. 4

   Find the angle: B = cos⁻¹(–1/2) = 120°.

Question

Write down the value of sin 30°

Worked Solution

1. 1

   sin 30° is one of the exact trigonometric values you need to know. In a right-angled triangle with a 30° angle, the ratio of the opposite side to the hypotenuse is exactly 1/2.

2. 2

   Therefore sin 30° = 1/2 = 0.5.