Answered

Explore a world of knowledge and get your questions answered on IDNLearn.com. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.

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 :

GinnyAnsweridn
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 are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.