classify the triangles as acute, obtuse and right: 10,25,15
Answers
Answer:
To help you visualize this, think of an equilateral triangle with sides of length 5. We know that this is an acute triangle. If you plug in 5 for each number in the Pythagorean Theorem we get 52+52=52 and 50>25. Therefore, if a2+b2>c2, then lengths a, b, and c make up an acute triangle. Conversely, if a2+b2<c2, then lengths a, b, and c make up the sides of an obtuse triangle. It is important to note that the length ‘‘c′′ is always the longest.
Using the Pythagorean Theorem
Determine if the following lengths make an acute, right or obtuse triangle.
1. 5, 6, 7
Plug in each set of lengths into the Pythagorean Theorem.
52+6225+3661 ? 72 ? 49>49
Because 61>49, this is an acute triangle.
2. 5, 10, 14
Plug in each set of lengths into the Pythagorean Theorem.
52+10225+100125 ? 142 ? 196<196
Because 125<196, this is an obtuse triangle.
3. 12, 35, 37
Plug in each set of lengths into the Pythagorean Theorem.
122+352144+12251369 ? 372 ? 1369=1369
Because the two sides are equal, this is a right triangle.