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

- 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. - Proof PT

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

Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - 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. - 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 ?. - 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. - 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. - 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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