# The right triangle altitude theorem - math word problems

The altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.$h=\sqrt{{c}_{1}{c}_{2}}$

Also known as a geometric mean theorem. Geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 39

- Without Euclid laws

Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws. - Euklid4

Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle. - Isosceles IV

In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - 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. - Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - Area of RT

In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of this triangle. - Area of RT

Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5. - 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 ?. - Proof PT

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

A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle. - Hypotenuse and height

In a right triangle is length of the hypotenuse c = 56 cm and height h_{c}= 4 cm. Determine the length of both trangle legs. - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Rhombus

It is given a rhombus of side length a = 19 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 5 cm and a_{2}= 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Euclid2

In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle. - Euclid3

Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg c_{b}= 39 cm. - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - 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. - 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. - Triangle ABC

Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle h_{AB}to the side AB.

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