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Q1(i):
In $\triangle ABC$, right-angled at $B$, $AB = 24$ cm, $BC = 7$ cm. Determine : (i) $\sin A, \cos A$

Solution :

Given: In $\triangle ABC$, $\angle B = 90^\circ$, $AB = 24\text{ cm}$, and $BC = 7\text{ cm}$.

To find: The values of $\sin A$ and $\cos A$.

B C A 7 cm 24 cm

Step 1: Determine the length of the hypotenuse ($AC$).

Since $\triangle ABC$ is a right-angled triangle, we apply the Pythagoras Theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

$AC^2 = AB^2 + BC^2$ [Pythagoras Theorem]

$AC^2 = (24)^2 + (7)^2$

$AC^2 = 576 + 49$

$AC^2 = 625$

$AC = \sqrt{625} = 25\text{ cm}$

Step 2: Define the trigonometric ratios for angle $A$.

For $\angle A$, the side opposite is $BC = 7\text{ cm}$, the side adjacent is $AB = 24\text{ cm}$, and the hypotenuse is $AC = 25\text{ cm}$.

The definitions of sine and cosine are:

$\sin A = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{BC}{AC}$

$\cos A = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{AB}{AC}$

Step 3: Calculate the values.

Substituting the known lengths into the ratios:

$\sin A = \frac{7}{25}$

$\cos A = \frac{24}{25}$

Final Answer: $\sin A = \frac{7}{25}$ and $\cos A = \frac{24}{25}$


More Questions from Class 10 Mathematics Introduction to Trigonometry EXERCISE 8.1


CBSE Solutions for Class 10 Mathematics Introduction to Trigonometry


Chapters in CBSE - Class 10 Mathematics


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