# 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. Geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 44

• RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• Right 24
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
• Right isosceles triangle
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
• Euclid2
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
• 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.
• Without Euclid laws
Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
• 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
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 - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
• 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.
• Same area
There is a given triangle. Construct a square of the same area.
• 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.
• 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.
• Conical area
A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
• Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of ​​this triangle.
• Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
• Proof PT
Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
• 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.
• Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.

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