Question

Given right triangle ABC, which of the following statements must be true?

A. sin A = cos C
B. tan A = sin B
C. cos A = tan B
D. cos A = sin C

Answer 1

In a right triangle ABC, the statement 'sin A = cos C' must be true because the sine of an angle is equal to the cosine of its complementary angle.

Step-by-step explanation:

Given right triangle ABC, the statement that must be true is A. sin A = cos C. This is because in a right triangle, the sine of an angle is equal to the cosine of the complementary angle, which is 90 degrees minus the original angle. Therefore, if angle A is acute, angle C as the other non-right angle in this triangle is its complement, making sin A equal to cos C.

The Pythagorean theorem states that in a right triangle with legs a and b and hypotenuse c, the relationship between these sides is a² + b² = c². Trigonometric functions like sine and cosine are based on the ratios of the sides of right triangles: the sine of an angle is the ratio of the opposite side to the hypotenuse, while the cosine is the ratio of the adjacent side to the hypotenuse.