Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right 7,15,21

Sagot :

sqdancefan

9514 1404 393

Answer:

  obtuse triangle

Step-by-step explanation:

The two shortest sides are 7, 15. Their sum is 7+15 = 22, which is longer than the longest side, so these lengths will form a triangle.

__

The "form factor" can be computed to be ...

  a^2 +b^2 -c^2 . . . . . where c = longest side

This value is ...

  7^2 +15^2 -21^2 = 49 +221 -441 = -167

This negative value indicates the largest angle is more than 90°, so the triangle is obtuse.

_____

Additional comment

This "form factor" has the same sign as the cosine of the largest angle. The cosine is negative for angles greater than 90°. The cosine of the angle is ...

  "form factor"/(2ab) = -167/210

  largest angle = arccos(-167/210) ≈ 142.678°

View image sqdancefan
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.