Photo AI

The diagram shows two right-angled triangles ABD and BCD, sharing a common side BD - OCR - GCSE Maths - Question 11 - 2018 - Paper 1

Question 11

The diagram shows two right-angled triangles ABD and BCD, sharing a common side BD. AD = 10 cm, BC = 12 cm and angle DBC = 60°. Work out the length of AB.

Worked Solution & Example Answer:The diagram shows two right-angled triangles ABD and BCD, sharing a common side BD - OCR - GCSE Maths - Question 11 - 2018 - Paper 1

Step 1

Determine the length of BD

96%

114 rated

Answer

In triangle BCD, we can use the cosine formula to find BD.

Using the cosine of angle DBC: $BC = BD / \cos(60^\circ)$

Substituting the known values: $12 = BD / 0.5$

Therefore, solving for BD gives: $BD = 12 * 0.5 = 6 \text{ cm}$

Step 2

Determine the length of AB

99%

104 rated

Answer

Now, knowing that AD = 10 cm and BD = 6 cm, we can find the length of AB using the Pythagorean theorem in triangle ABD:

Using: $AD^2 = AB^2 + BD^2$

Substituting the known values: $10^2 = AB^2 + 6^2$ $100 = AB^2 + 36$

Rearranging gives: $AB^2 = 100 - 36$ $AB^2 = 64$

Taking the square root: $AB = \sqrt{64} = 8 \text{ cm}$

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;