# The right triangle altitude theorem - 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.

Also known as geometric mean theorem.

1. Right Δ
Right triangle has 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. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
9. 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.
10. Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
11. 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.
12. Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
13. Goat and circles
What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
14. Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
15. RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
16. 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.
17. 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.
18. 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.
19. 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 cb = 39 cm.
20. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.

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