Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

For positive acute angles AA and B,B, it is known that \sin A=\frac{8}{17}sinA= 17 8 ​ and \cos B=\frac{24}{25}. CosB= 25 24 ​. Find the value of \sin(A+B)sin(A+B) in simplest form

Sagot :

sqdancefan

Answer:

  sin(A+B) = 297/425

Step-by-step explanation:

This problem involves a couple of Pythagorean triples, and the trig identity for the sine of the sum of angles.

The Pythagorean triples involved are {8, 15, 17} and {7, 24, 25}. These tell us the other trig functions of the given angles:

  sin(A) = 8/17   ⇔   cos(A) = 15/17

  cos(B) = 24/25   ⇔   sin(B) = 7/25

The trig identity we're using is ...

  sin(A+B) = sin(A)cos(B) +cos(A)sin(B)

  sin(A+B) = (8/17)(24/25) +(15/17)(7/25)

  [tex]\sin(A+B)=\dfrac{8\cdot24+15\cdot 7}{17\cdot25}\\\\\boxed{\sin(A+B)=\dfrac{297}{425}}[/tex]

_____

Check

  A = arcsin(8/17) ≈ 28.072°

  B = arccos(24/25) ≈ 16.260°

  sin(A+B) = sin(44.332°) ≈ 0.6988235

  sin(A+B) = 297/425

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.