8th grade (13y) + The right triangle altitude theorem - examples

1. Right Δ A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
2. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
3. Area of RT Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
4. Rhombus It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
5. Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
6. Rectangle In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
7. Tangents To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
8. Circle in rhombus In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
9. Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.

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