The right triangle altitude theorem - practice problems - page 2 of 4
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: 62
- Cableway
The 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 at the base station. - RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Right 24
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you. - Perpendicular 32733
Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate: A hypotenuse segment cb, side a, a hypotenuse segment ca, and a height of triangle v - 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 - 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|). - Perpendicular 5667
The perpendicular projections hung on the diaphragm are 3.1 cm and 6.3 cm long in a right triangle. Calculate the perimeter of this triangle. The result is rounded to the nearest hundredth of an inch. - Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Right isosceles triangle The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two equal segments. The length of one segment is 5 cm. What is the area of the triangle?
- 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. - 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-angled 82471
In the right-angled triangle ABC, the lengths a = 7.2 cm, and b = 10.4 cm are dropped. Do the math a) lengths of the sections of the hypotenuse b) height 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 center. - Right-angled 81989
Using Euclid's Theorems and Pythagoras' Theorem, complete the following parameters describing a right-angled triangle ABC with a right angle at vertex C if we know b=10, cb=8 - Triangle ABC
In a triangle ABC with the side BC of length 2 cm. Point K is 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 point K. Determine the lengths of the sides AB, AC triangle A - Right-angled 81019
In the right-angled triangle ABC (AB is the hypotenuse), a : b = 24 : 7, and the height to the side c = 12.6 cm applies. Calculate the lengths of the sides of triangle ABC. - Hypotenuse 72524
We know the height of the hypotenuse h = 4cm and the hypotenuse c = 19cm in a right triangle. How to calculate the segments of legs - sections on the hypotenuse c1, c2 - Medians in right triangle
It is given a right triangle, and angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. How to calculate the length of the sides? - Right Δ
A right triangle has the length of one leg 72 cm and the hypotenuse 90 cm size. Calculate the height of the triangle. - Right-angled 3147
In a right-angled triangle ABC, the height of side c has a length of 6 cm. The letter D indicates the heel of the height. Line segment AD is 8 cm long. Calculate the area of triangle ABC. ( example on Monitor 9 )
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