- a.The connection between the leg and the tabletop forms the
right angle of this triangle.The length of the leg and the length of
the top are the legs of the triangle, and the question wants to know
the distance of the hypotenuse. Plug the known measurements into
the Pythagorean theorem: 3^2 + 4^2 = c^2. 9 + 16 = c^2. 25 = c^2. 5 = c.
If you chose answer d, you forgot to take the square root of 25. If
you chose answer b, you added the legs together without squaring
them first. - b.The first plane is actually this triangle’s right vertex. The
distance between Dorothy and the second plane is the hypotenuse.
Plug the known measurements into the Pythagorean theorem:
3002 + b^2 = 500^2. 90,000 + b^2 = 250,000. b^2 = 160,000. b= 400. Notice
that if you divided each side by 100, this is another 3-4-5 triangle. - d.The bases of Timmy’s walls form the legs of this right triangle.
The hypotenuse is unknown. Plug the known measurements into
the Pythagorean theorem: 10^2 + 15^2 = c^2. 100 + 225 = c^2. 325 = c^2.
325 = c.
Set 40
- ΔSBT and ΔEFD are congruent to each other (Side-Angle-Side
theorem) and similar to ΔBDC (Angle-Angle theorem). - x= 4.Because ΔBCD is an isosceles right triangle, BDis con-
gruent to CD. Plug 3x, 3x,and 4 18 into the Pythagorean
theorem: (3x)^2 + (3x)^2 = (4 18 )^2. 9x^2 + 9x^2 = 288.
18 x^2 = 288. x^2 = 16. x= 4. - y= 6 2 .In the question above, you found x= 4. Therefore, CD =
- Since BT = DT, they both equal 6. Since BT = FD = FE, FD =
FE = 6. Plug 6, 6, and yinto the Pythagorean theorem. - Remember SU≅UV, so to find the measurement of SU, plug the
given measurements of ΔSUY into the Pythagorean theorem. 7^2 +
b^2 = (5 2 )^2. 49 + b^2 = 50. b^2 = 1. b= 1 = 1.
501 Geometry Questions