Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all 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.