anonymous
  • anonymous
An acute triangle has side 8 and 15. How many possible integral lengths are there for the third side?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
wolf1728
  • wolf1728
The 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.