Answers
Set 38
- b.This is a popular triangle, so know it well. A 3-4-5 triangle is a
right triangle. Apply the Pythagorean theorem: a^2 + b^2 = c^2. 3^2 + 4^2
= 5^2. 9 + 16 = 25. 25 = 25. - a.Plug the given measurements into the Pythagorean theorem:
122 + 13^2 = 16^2. 144 + 169 = 256. 313 > 256. Acute. - a.Plug the given measurements into the Pythagorean theorem
(the largest side is always cin the theorem): 15^2 + 17^2 = 22^2. 225 +
289 = 484. 514 > 484. When the sum of the smaller sides squared
is greater than the square of the largest side, then the triangle is
acute. - d.In order for a triangle to exist, the sum of the length of any two
sides needs to be longer than the length of third side. The given
sides, 8, 10, and 18, do not make a triangle since the sum of the
smaller two sides is only 18, which is equal to, but not greater than,
the third side. - a.Plug the given measurements into the Pythagorean theorem:
122 + 12^2 = 15^2. 144 + 144 = 225. 288 > 225. Acute. - d.The Pythagorean theorem does not include any angles. Without
a third side or a definite right angle, this triangle cannot be
determined. - b.This is also a 3–4–5 triangle. Simplify the measurement of each
side by dividing 12, 16, and 20 by 4: ^142 = 3. ^146 = 4. ^240 = 5. - d.The corner forms the right angle of this triangle; Eva and Carr
walk the distance of each leg, and the question wants to know the
hypotenuse. Plug the known measurements into the Pythagorean
theorem: 5^2 + 6^2 = c^2. 25 + 36 = c^2. 61 = c^2. 61 = c.
501 Geometry Questions