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ABC is a right-angled triangle - OCR - GCSE Maths - Question 5 - 2019 - Paper 6

Question 5

ABC is a right-angled triangle. AB = 20 cm and BC = 37 cm. Calculate angle BAC.

Worked Solution & Example Answer:ABC is a right-angled triangle - OCR - GCSE Maths - Question 5 - 2019 - Paper 6

Step 1

Step 1: Identify the Triangle and Given Information

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Answer

We have a right-angled triangle ABC, where:

AB = 20 cm (the opposite side)
BC = 37 cm (the hypotenuse)

We need to find angle BAC.

Step 2

Step 2: Use the Sine Function

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Answer

To find angle BAC, we can use the sine function, which relates the opposite side and the hypotenuse:

$\sin(BAC) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AB}{BC}$

Substituting the values:

$\sin(BAC) = \frac{20}{37}$

Step 3

Step 3: Calculate BAC

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Answer

Now, to find angle BAC, we take the inverse sine:

$BAC = \arcsin\left(\frac{20}{37}\right)$

Using a calculator:

$BAC \approx 34.89^\circ$

Step 4

Step 4: Round the Answer

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Answer

Finally, rounding this to one decimal place gives:

$BAC \approx 34.9^\circ$

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ABC is a right-angled triangle - OCR - GCSE Maths - Question 5 - 2019 - Paper 6

Worked Solution & Example Answer:ABC is a right-angled triangle - OCR - GCSE Maths - Question 5 - 2019 - Paper 6

Step 1: Identify the Triangle and Given Information

Step 2: Use the Sine Function

Step 3: Calculate BAC

Step 4: Round the Answer

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