Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

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 :

GinnyAnswer
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]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.