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

1. Find the length of BD using triangle BCD

96%

114 rated

Answer

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

Using the formula: $BD = BC \cdot \cos(60^{\circ})$ Substituting the values: $BD = 12 \cdot 0.5 = 6 \text{ cm}$

Step 2

2. Find the length of AB using triangle ABD

99%

104 rated

Answer

In triangle ABD, we can now use the Pythagorean theorem to find AB:

The side AD = 10 cm and we have found BD = 6 cm. Therefore, we can apply: $AB^2 + BD^2 = AD^2$ Substituting the known values: $AB^2 + 6^2 = 10^2$ This results in: $AB^2 + 36 = 100$ Thus: $AB^2 = 64$ Taking the square root gives: $AB = 8 \text{ cm}$

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

;