Pythagorean theorem - 8th grade (13y) - math problems

Number of problems found: 443

Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
The rotating
The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
Proof PT
Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
Height 2
Calculate the height of the equilateral triangle with side 27.
Triangle
Can an equilateral triangle have a right angle?
Distance
Wha is the distance between the origin and the point (18; 22)?
Height
Is right that in any right triangle height is less or equal half of the hypotenuse?
Distance
Calculate distance between two points X[18; 19] and W[20; 3].
Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
Cube diagonal
Determine the length of the cube diagonal with edge 37 mm.
Body diagonal
Calculate the length of the body diagonal of the 6cm cube.
Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
Trio 2
Decide whether a trio of numbers is the side of a right triangle: 26,24,10.
Square
Calculate area of the square with diagonal 64 cm.
Height
Calculate height of the equilateral triangle if its perimeter is 8?
Equilateral triangle v2
Equilateral triangle has a perimeter 36 dm. What is its area?
4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?