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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]$\cos (C) =$[/tex] [tex]$\square$[/tex]

If [tex]$\cos (C) = \frac{20}{25}$[/tex], the value of [tex]$\sin (A) =$[/tex] [tex]$\square$[/tex]



Answer :

GinnyAnswer
In a right triangle, the two non-right angles, \( A \) and \( C \), are complementary. That is, \( A + C = 90^\circ \). For complementary angles in a right triangle, the sine of one angle is equal to the cosine of the other angle.

Given:
1. \(\sin(A) = \frac{24}{25}\)
2. \(\cos(C) = \frac{20}{20}\)

Step-by-Step Solution:

1. \(\sin(A) = \frac{24}{25}\):
- Since \( A \) and \( C \) are complementary angles, \(\cos(C) = \sin(A)\).
- Therefore, \(\cos(C) = \frac{24}{25}\).

2. \(\cos(C) = \frac{20}{20}\):
- Simplify \(\frac{20}{20}\): \(\frac{20}{20} = 1\).
- Since \( A \) and \( C \) are complementary angles, \(\sin(A) = \cos(C)\).
- Therefore, \(\sin(A) = 1\).

Thus:

[tex]\[ \cos(C) = \frac{24}{25} \][/tex]

[tex]\[ \sin(A) = 1 \][/tex]

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