# 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. The geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 48

• Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5cm and ml = 15 cm.
• Euclid theorems Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• Sides of the triangle Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
• Cableway Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
• Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
• Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
• Circles In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
• 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
• 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.
• 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.
• 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 (|PB|)/(|DP|).
• 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.

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