Question

For the given statements select the correct option.

Assertion : The value of $sin\theta =\frac{4}{3}$ in not possible.

Reason : Hypotenuse is the largest side in any right angled triangle.

• A. Assertion is false but reason is true
• B. Assertion is true but reason is false.
• C. Both assertion and reason are true but reason is not the correct explanation of assertion.
• D. Both assertion and reason are true and reason is the correct explanation of assertion.

Answer 1

The correct option is D

Both assertion and reason are true and reason is the correct explanation of assertion.

Let us, consider $sin\theta =\frac{4}{3}$

We know that,
$sin\theta =\frac{Height}{Hypotnuse}$

Now, considering the above data,
Height = 4 unit and Hypotnuse = 3 unit

We also kow that, the triangle must be right angled triangle to get the value of sinθ

So, now apply the pythagoras theorem to get the base of the triangle,
we get base = $\sqrt{3^2-4^2}\sqrt{9-16}\sqrt{-7}$
Which is not possible.

Hence, assertion is true and to follow the pythagoras theorem the hypotnuse has to be the largest side in the triangle.

Therefore, reason is also correct and reason is the correct explanation for the assertion.