**\#1.) In right triangle $$ A B C, m \angle A=90^{\circ} $$. Which of the following is true? a) $$ \sin B=\sin C $$ b) $$ \sin C=\cos C $$ c) $$ \sin B=\cos C $$ d) $$ \cos C= an B $$

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**\#1.) In right triangle $$ A B C, m \angle A=90^{\circ} $$. Which of the following is true? a) $$ \sin B=\sin C $$ b) $$ \sin C=\cos C $$ c) $$ \sin B=\cos C $$ d) $$ \cos C=	an B $$

UpStudy AI · Accepted Answer

Given that triangle $$ ABC $$ is right with $$ m \angle A = 90^{\circ} $$, the remaining angles satisfy

$$
m \angle B + m \angle C = 90^{\circ}.
$$

This implies that $$ \angle B $$ and $$ \angle C $$ are complementary. Using the complementary angle relationships in trigonometry, we have:

$$
\sin B = \cos (90^{\circ} - \angle B).
$$

Since $$ 90^{\circ} - \angle B = \angle C $$, it follows that

$$
\sin B = \cos C.
$$

Thus, the correct statement is:

c) $$ \sin B = \cos C $$.
$$ \sin B = \cos C $$

**\#1.) In right triangle \( A B C, m \angle A=90^{\circ} \). Which of the following is true? a) \( \sin B=\sin C \) b) \( \sin C=\cos C \) c) \( \sin B=\cos C \) d) \( \cos C=\tan B \)

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