Photo AI
The diagram shows a right-angled triangle - OCR - GCSE Maths - Question 22 - 2023 - Paper 2
Question 22
The diagram shows a right-angled triangle. a cm 14 cm 30° Work out the value of a. a = .........................................
Worked Solution & Example Answer:The diagram shows a right-angled triangle - OCR - GCSE Maths - Question 22 - 2023 - Paper 2
Step 1
Work out the value of a
Answer
To find the length of side 'a' in the right-angled triangle, we can use trigonometric ratios. Since we have the angle (30°) and the side opposite to it (14 cm), we can use the sine function:
-
The formula for sine in a right triangle is:
-
Here, we know:
- Opposite side = 14 cm
- Angle ( \theta = 30° )
-
Therefore, according to the sine function:
-
We know that ( \sin(30°) = \frac{1}{2} ). Substituting this into the equation:
-
To solve for 'a', we cross-multiply:
-
Thus, we find:
So, the value of 'a' is:
a = 28 cm