Question

In $△OPQ$ right angled at $P,OP=7cm$ and $OQ-PQ=1cm$ then the value of $\sin Q$.

• A. $\frac{7}{25}$
• B. $\frac{24}{25}$
• C. $1$
• D. $noneofthese$

Answer 1

The correct option is A $\frac{7}{25}$

The length of $PQ$ is $24$ cm and the length of $OQ$ is $25$ cm.

Step-by-step explanation:

It is given that in triangle $OPQ$ right angle at $P,OP=7$ cm, $OQ-PQ=1$ cm.

Since the difference of $OQ$ and $PQ$ is $1,$ therefore $OQ$ is $1$ more than $PQ.$

Let the length of $PQ$ be $x$ cm. So, the length of $OQ$ is $x+1$ cm.

Using Pythagoras theorem,

The value of $x$ is $24$. So, the length of PQ is $24$ cm.

The length of $OQ$ is $x+1=24+1$

The length of $OQ$ is $25$ cm.

Therefore the length of $PQ$ is $24$ cm and the length of $OQ$ is $25$ cm.

$sin\left(\Theta \right)=\frac{Opposite}{Hypotenuse}$

$\sin Q=\frac{OP}{OQ}=\frac{7}{25}$