Question

In triangle $ABC$ if $\angle B = 90^\circ$, $AB = 5$ cm and $BC = 12$ cm, the value of $\sin A$ will be :

• A. 5/13
• B. 5/12
• C. 12/13
• D. 13/17

Hint:

5, 12, 13 is a very common Pythagorean triplet! Memorizing triplets like (3,4,5) and (5,12,13) saves a lot of calculation time.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In a right-angled triangle, $\sin \theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$. To find the hypotenuse, we use the Pythagoras theorem.

Step 2: Finding Hypotenuse (AC):
$$AC^2 = AB^2 + BC^2$$
$$AC^2 = 5^2 + 12^2$$
$$AC^2 = 25 + 144 = 169$$
$$AC = \sqrt{169} = 13 \text{ cm}$$
Step 3: Calculating sin A:
For angle $A$, the perpendicular side is the opposite side $BC$, and the hypotenuse is $AC$:
$$\sin A = \frac{BC}{AC} = \frac{12}{13}$$
Step 4: Final Answer:
The value of $\sin A$ is 12/13.