Question

In the figure, the value of cosec A is

• A. \(\frac{12}{13}\)
• B. \(\frac{13}{5}\)
• C. \(\frac{13}{12}\)
• D. \(\frac{5}{13}\)

Answer 1

The Correct Option is C

To solve the problem, we need to determine the value of \( \cosec A \) in the given right triangle. Let us analyze the figure step by step.

Step 1: Understand the Triangle The given triangle is a right triangle with:
\( \angle C = 90^\circ \) (right angle),
Hypotenuse \( AB = 13 \),
Side \( AC = 5 \),
Side \( BC = 12 \).

We are asked to find \( \cosec A \), where \( \cosec A \) is the reciprocal of \( \sin A \): \[ \cosec A = \frac{1}{\sin A} \] and \[ \sin A = \frac{\text{opposite side}}{\text{hypotenuse}}. \]

Step 2: Identify the Opposite and Hypotenuse for \( \angle A \) In \( \triangle ABC \):
The side opposite to \( \angle A \) is \( BC = 12 \).
The hypotenuse is \( AB = 13 \). Thus: \[ \sin A = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AB} = \frac{12}{13}. \]

Step 3: Calculate \( \cosec A \) Since \( \cosec A \) is the reciprocal of \( \sin A \): \[ \cosec A = \frac{1}{\sin A} = \frac{1}{\frac{12}{13}} = \frac{13}{12}. \] Final Answer: \(\frac {13}{12}\)