Question

Select the correct answer.

A right angle triangle where ABC angle is 90° and angle ACB is 45°.

Which trigonometric ratio will not have the same value as sin A?

A.
cos A

B.
sin C

C.
tan C

D.
cos C

Answer 1

In a 45-45-90 right triangle, the sine and cosine for angles A and C are equal as both are 45°. However, the tangent of angle C (tan C) will always be 1, which is different from the sine of angle A (sin A), making C. tan C the correct answer. Therefore, the correct answer is C. tan C.

Step-by-step explanation:

If we have a right-angle triangle where angle ABC is 90° and angle ACB is 45°, then by definition triangle ABC is a 45-45-90 triangle, also known as an isosceles right triangle. Because the two non-right angles in this triangle are equal, trigonometric ratios for these angles will also be equal. This includes the sine, cosine, and tangent ratios. The sine of angle A (sin A) will be equal to the cosine of angle C (cos C), which is also angle A in this case, since they are both 45° angles.

However, the trigonometric ratio that will not have the same value as sin A is the tangent of angle C (tan C). In a 45-45-90 triangle, while sine and cosine are equal due to the isosceles nature, the tangent ratio, which is the ratio of the opposite side to the adjacent side, will always be 1 for a 45° angle, which differs from the sine and cosine values that are less than 1. Therefore, the correct answer is C. tan C.