Question

Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

Answer 1

The sine and cosine are equal for 45 degrees.
Choose the triangle that has a 45-deg angle.

Answer 2

we have to consider a triangle whose acute angle measure is 45° so that the sine and cosine ratios are equal.

Explanation:

We need to consider a right angled triangle such that the measure of one of angle is 90° ,the second angle is 45° and hence the third angle could be found by using the fact that the sum of all the angles is 180°.

Hence we get the third angle measure to be 45°

( ∠1+∠2+∠3=180°

90+45+∠3=180

∠3=180-(90+45)

∠3=45° )

so in the right angled triangle if we use our trignometric identity along either angle 2 or angle 3 we get;

sin 45°=
`(1)/(√(2) )`

and cos 45°=
`(1)/(√(2) )`

Hence the sine and cosine angle are equal.

So we have to consider a triangle whose acute angle measure is 45° so that the sine and cosine ratios are equal.