Prove that

Question:

If $\sec \theta=\frac{25}{7}$ then $\sin \theta=$ ?

(a) $\frac{7}{25}$

(b) $\frac{24}{25}$

(c) $\frac{7}{24}$

(d) $\frac{24}{7}$

 

Solution:

Given: $\sec \theta=\frac{25}{7}$

Since, $\sec \theta=\frac{H}{B}$

$\Rightarrow B=7$ and $H=25$

Using Pythagoras theorem,

$P^{2}+B^{2}=H^{2}$

$\Rightarrow P^{2}+(7)^{2}=(25)^{2}$

$\Rightarrow P^{2}=625-49$

$\Rightarrow P^{2}=576$

$\Rightarrow P=24$

Therefore,

$\sin \theta=\frac{P}{H}=\frac{24}{25}$

Hence, the correct option is (b).

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