Question

1. If sin A = 24/25, then the value of cos A is​

Answer 1

Answer:

This is your answer

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Answer 2

Answer:

The value of $cosA$ is $\frac{7}{25}$.

Step-by-step explanation:

Consider a right triangle $ABC$.

Recall the trigonometric identities for triangle $ABC$,

$sinA=\frac{Perpendicular}{hypotenuse}$

⇒ $sinA=\frac{BC}{AC}$ ...... (1)

$cosA=\frac{Base}{hypotenuse}$

⇒ $cosA=\frac{AB}{AC}$ ...... (2)

It is given that $sinA=\frac{24}{25}$ ...... (3)

Then, from (1) and (3), we get

$BC=24$ and $AC=25$

In Δ$ABC$, by Pythagoras theorem,

⇒ $AB^2=AC^2-BC^2$

⇒ $AB^2=25^2-24^2$

⇒ $AB^2=625-576$

⇒ $AB^2=49$

⇒ $AB=7$

From (2), we get

$cosA=\frac{7}{25}$

Therefore, the value of $cosA$ is $\frac{7}{25}$.

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