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

Number of problems found: 421

Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
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
Proof PT
Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
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)
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 ?
Triangle
Can be rectangular triangle equilateral?
Height
Is right that in any right triangle height is less or equal half of the hypotenuse?
Trio 2
Decide whether a trio of numbers is the side of a right triangle: 26,24,10.
Distance
Calculate distance between two points X[18; 19] and W[20; 3].
Distance
Wha is the distance between the origin and the point (18; 22)?
Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
Is right triangle or not
If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
Is right?
Is a triangle with sides 51, 56, and 77 right triangle?
Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
Height
Calculate height of the equilateral triangle if its perimeter is 8?
Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
Windbreak
A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
The ladder
The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
Park
In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.