Question

In: Advanced Math

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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