A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
An acute triangle has side 8 and 15. How many possible integral lengths are there for the third side?
anonymous
 one year ago
An acute triangle has side 8 and 15. How many possible integral lengths are there for the third side?

This Question is Closed

wolf1728
 one year ago
Best ResponseYou've already chosen the best response.2The third side has to be greater than 7, otherwise a triangle can't be formed. The third side has to be less than 17, otherwise it will be a right triangle or an obtuse triangle. So, that leaves us with possible side lengths of 8, 9 10, 11, 12, 13, 14, 15 and 16 We can use the Law of Cosines to determine if Angle B is less than 90 degrees. cos(B) = (8^2 + 8^2 15^2) / (2*8*8) cos(B) = 0.7578125 Angle B = 139.27 Degrees cos(B) = (9^2 + 8^2 15^2) / (2*9*8) cos(B) = .555555555 cos(B) = 123.75 Degrees We continue with this until we have side a = 13 where angle B equals 87.796 So, the possible lengths for side "a" are 13, 14, 15 and 16
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.