Question

in the given figure, δabc is a right triangle. what is true about δabc? a. sin(a) = cos(c) and cos(a) = cos(c) b. sin(a) = cos(a) and sin(c) = cos(c) c. sin(a) = cos(c) and cos(a) = sin(c) d. sin(a) = sin(c) and cos(a) = cos(c)

Explanation:

In right triangle \( \Delta ABC \) (assuming right angle at B), angles A and C are complementary (\( A + C = 90^\circ \)). For complementary angles, \( \sin(\theta) = \cos(90^\circ - \theta) \). Thus, \( \sin(A) = \cos(C) \) and \( \cos(A) = \sin(C) \), which matches option C. Other options have incorrect equalities (e.g., \( \cos(A)
eq \cos(C) \) in A, \( \sin(A)
eq \cos(A) \) unless \( A=45^\circ \) in B, etc.).

Answer:

C. sin(A) = cos(C) and cos(A) = sin(C)