# 9th grade (14y) + Pythagorean theorem - examples

Pythagorean theorem is the base for the right triangle calculator.- Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - 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) - Forces on earth directions

A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Isosceles triangle

Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm. - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Logs

Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm? - Right Δ

Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm. - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - Square diagonal

Calculate the length of diagonal of the square with side a = 23 cm. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Acreage

What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ? - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm. - Garden

Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?

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