A triangle has sides a, b, and c. Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=3, b=4, and c=5.
Option A: Yes, a right triangle can be formed.
Option B: No, a right triangle cannot be formed.
Choose 1 for Option A or 2 for Option B.
(1 point)
1
Use the image to answer the question.
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(1 point)
To apply the Pythagorean Theorem, we can treat the line connecting the two points as the hypotenuse of a right triangle. The length between the two points can be found by calculating the distance between their x-coordinates and y-coordinates.
The x-coordinate difference is: 7 - 3 = 4
The y-coordinate difference is: 8 - 2 = 6
Using the Pythagorean Theorem, the length between the two points is:
√(4^2 + 6^2) = √(16 + 36) = √52 ≈ 7.21
Therefore, the length between the two points is approximately 7.21.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The front and left faces of the pyramid and base are visible. The back and right faces are not visible. The back and right base edges are not visible but their position is indicated by a dashed line. The left base edge shows a length of 16 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and shows a height of 15. A right angle is indicated where the dotted height line meets the base.
Find the slant height of the square pyramid.
(1 point)
units
To find the slant height of the square pyramid, we can use the Pythagorean Theorem. In the right triangle formed by the slant height, height, and one-half of the base, the height is the length of the dotted line (15), and one-half of the base is half of 16 (8).
Let's denote the slant height as "s". Using the Pythagorean Theorem, we have:
s^2 = 8^2 + 15^2
s^2 = 64 + 225
s^2 = 289
Taking the square root of both sides:
s = √289
s = 17
Therefore, the slant height of the square pyramid is 17 units.