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A right triangle [tex]\(ABC\)[/tex] has complementary angles [tex]\(A\)[/tex] and [tex]\(C\)[/tex].

If [tex]\(\sin(A)=\frac{24}{25}\)[/tex], the value of [tex]\(\cos(C)= \boxed{}\)[/tex]

If [tex]\(\cos(C)=\frac{20}{29}\)[/tex], the value of [tex]\(\sin(A)= \boxed{}\)[/tex]

Sagot :

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A right triangle [tex]\( ABC \)[/tex] has complementary angles [tex]\( A \)[/tex] and [tex]\( C \)[/tex].

1. To determine the value of [tex]\(\cos(C)\)[/tex] when [tex]\(\sin(A) = \frac{24}{25}\)[/tex]:

- Since [tex]\( A \)[/tex] and [tex]\( C \)[/tex] are complementary angles, we know that [tex]\( \sin(A) = \cos(C) \)[/tex].
- Thus, if [tex]\(\sin(A) = \frac{24}{25}\)[/tex], then [tex]\(\cos(C) = \frac{24}{25}\)[/tex].

2. To determine the value of [tex]\(\sin(A)\)[/tex] when [tex]\(\cos(C) = \frac{20}{29}\)[/tex]:

- Similarly, since [tex]\( A \)[/tex] and [tex]\( C \)[/tex] are complementary angles, we know that [tex]\( \cos(C) = \sin(A) \)[/tex].
- Thus, if [tex]\(\cos(C) = \frac{20}{29}\)[/tex], then [tex]\(\sin(A) = \frac{20}{29}\)[/tex].

Therefore, the values are:

[tex]\[ \cos(C) = 0.96 \][/tex]
[tex]\[ \sin(A) = 0.6896551724137931 \][/tex]
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