Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Solve the triangle.
B = 36°, a = 41, c = 17 (5 points)

Sagot :

iLoveMathAndEnglish

Answer:

b = 29.0, A = 123.9°, C = 20.1°

sqdancefan

9514 1404 393

Answer:

  b = 29.0; A = 123.9°, C = 20.1°

Step-by-step explanation:

The given angle lies between the given sides, so the Law of Cosines is the appropriate relation.

  b² = a² +c² -2ac·cos(B)

  b² = 1681 +289 -1394cos(36°) ≈ 842.2303

  b ≈ √842.2303 ≈ 29.021

__

The Law of Sines can be used to find angle C:

  sin(C)/c = sin(B)/b

  C = arcsin(c/b·sin(B)) = arcsin(17/29.021×sin(36°))

  C ≈ 20.1°

  A = 180° -36° -20.1° = 123.9°

The remaining side and angles are ...

  b ≈ 29.0; A ≈ 129.9°; C ≈ 20.1°

_____

Additional comment

By choosing to find the smaller angle C first, we avoid having to deal with the ambiguity associated with the arcsine when the angle is greater than 90°.

View image sqdancefan
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.