# Find the values of sin θ, cos θ, and tan θ for the given right triangle. Give the exact values.

Find the values of sin θ, cos θ, and tan θ for the given right triangle. Give the exact values.

## Solutions

##### Expert Solution

since,

$$\sin \theta=\frac{\text { height }}{\text { hypotenuse }}$$

Where height of the triangle is that side which is opposite to the angle $$\theta$$

Hence,

$$\sin \theta=\sqrt{\frac{24}{25}}$$

since,

$$\cos \theta=\frac{\text { base }}{\text { hypotenuse }}$$

Where base of the triangle is that side on which the angle is inclined

Hence,

\begin{aligned} \cos \theta &=\frac{\sqrt{25^{2}-24^{2}}}{25} \\ &=\frac{\sqrt{625-576}}{25} \\ &=\frac{\sqrt{49}}{25} \\ &=\frac{7}{25} \end{aligned}

since,

$$\tan \theta=\frac{\text { height }}{\text { base }}$$

Where height of the triangle is that side which is opposite to the angle $$\theta$$ and base of the triangle

is that side on which the angle is inclined

Hence,

$$\tan \theta=\sqrt{\frac{24}{7}}$$

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