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=c1c2
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: 59
- 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? - 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. - 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 hc = 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 vc = 5 cm. - 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. - 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 cb = 39 cm. - 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 hc=3 cm on the hypotenuse c? - 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? - Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides into 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. - Quadrilateral 78874
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime
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