In a , right angled at B, AB = 24cm, BC = 7cm. Determine: A, A - Vidyadip

Question

In a $\triangle\text{ABC},$ right angled at B, AB = 24cm, BC = 7cm. Determine:
$\sin \text{A}, \cos \text{A}$

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Answer

$\triangle\text{ABC}$ is right angled at B
AB = 24cm, BC = 7cm.
Let 'x' be the hypotenuse,
By applying Pythagoras
$\text{AC}^2=\text{AB}^2+\text{BC}^2$
$\text{x}^2=24^2+7^2$
$\text{x}^2=576+49$
$\text{x}^2=625$
$\text{x}=25$
$\sin\text{A},\cos\text{A}$
At $\angle\text{A,}$ opposite side = 7
adjacent side = 24
hypotenuse = 25
$\sin\text{A}=\frac{\text{opposite side}}{\text{hypotenuse}}=\frac{7}{25}$
$\cos\text{}A=\frac{\text{adjacent side}}{\text{hypotenuse}}=\frac{24}{25}$

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