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.

Number of problems found: 55

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
Construct 61253
Using Euclid's theorem, construct a line of length √15.
Altitude angles
Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit
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?
Perpendicular 32733
Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate cb, a, ca, v?
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.
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.
Free space in the garden
The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
Medians in right triangle
It is given a right triangle, 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?
Isosceles triangle 9
Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
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?
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?
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.
Circumscribed 6568
In a right triangle ABC with a right angle at the vertex C, it is given: a = 17cm, Vc = 8 cm. Calculate the length of the sides b, c, its area S, the perimeter o, the length of the radii of the circles of the triangle circumscribed by R and inscribed r an
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.
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.
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.

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