Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields 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]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.