# The right triangle altitude theorem - practice 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=c_{1}c_{2} $

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

Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 63

- Euclid2

The ABC right triangle with a right angle at C is side a=29 and height v=17. Calculate the perimeter of the 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. - Height of right RT

The right triangle ABC has a hypotenuse c 9 cm long and a part of the hypotenuse cb = 3 cm. How long is the height of this right triangle? - Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - 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. - 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 triangle legs. - Euclid 5

Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height v_{c}= 5 cm. - Triangle ABC

Right triangle ABC with right angle at the C, |BC|=19, |AB|=32. Calculate the height of the triangle h_{AB}to the side AB. - Euclid3

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

In the rhombus is an inscribed circle. Contact points of touch divide the sides into parts of length 14 mm and 9 mm. Calculate the circle area. - Proof PT

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

The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of this triangle. - Euclid1

The right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - RT triangle and height

Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm. - Spruce height

How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree? - Without Euclid laws

Right triangle ABC with a 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. - Area of RT

Calculate the right triangle area that hypotenuse has length 14, and one hypotenuse segment has length 5. - RT - hypotenuse and altitude

The right triangle BTG has hypotenuse g=117 m, and the altitude to g is 54 m. How long are hypotenuse segments? - 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. - Sides of the triangle

Calculate triangle sides where its area is S = 84 cm² and a = x, b = x + 1, xc = x + 2

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