Question

What is the ratio of the hypotenuse to the opposite side?

Answer 1

the ratio is 2:1 of hypotenuses

Answer 2

The ratio of the hypotenuse to the opposite side is  $cosec\theta=\frac{1}{sin\theta}$.

Given:

The hypotenuse and the opposite side.

To Find:

The ratio of the hypotenuse to the opposite side.

Solution:

The ratio of the hypotenuse to the opposite side is $cosec\theta=\frac{1}{sin\theta}$.

$cosec\theta$ and $sin\theta$ are trigonometric ratios. There is a total of six trigonometric ratios. These are $sin\theta,\,cos\theta,\,tan\theta,\,cosec\theta,\,sec\theta,\,cotangent\theta$.

These ratios are calculated using a right-angled triangle.

It is clear from the figure that the ratio of the opposite side to the hypotenuse is $sin\theta$ so the ratio of the hypotenuse to the opposite side is $cosec\theta$.

Thus, the ratio of the hypotenuse to the opposite side is  $cosec\theta=\frac{1}{sin\theta}$.

#SPJ6