# The right triangle altitude theorem - math 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: 47

• Euklid4
The 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.
• Without Euclid laws
Right triangle ABC with right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws.
• Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
• 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 ?.
• Rhombus
It is given a rhombus of side length a = 19 cm. Touchpoints of inscribed circle divided his sides into sections a1 = 5 cm and a2 = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
• Right Δ
A right triangle has the length of one leg 11 cm and the hypotenuse 61 cm size. Calculate the height of the triangle.
• Area of RT
Calculate the right triangle area that hypotenuse has length 14, and one hypotenuse segment has length 5.
• 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.
• Proof PT
Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
• Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of ​​this triangle.
• Euclid2
In the right triangle ABC with a right angle at C is given side a=29 and height v=17. 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 cb = 39 cm.
• Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
• 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.
• RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• 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.
• Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
• Euclidean distance
Calculate the Euclidean distance between shops A, B, and C, where: A 45 0.05 B 60 0.05 C 52 0.09 The first figure is the weight in grams of bread, and the second figure is the USD price.
• 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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