# The right triangle altitude theorem - high school - 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: 38

• 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.
• 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.
• 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?
• 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.
• 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.
• Same area There is a given triangle. Construct a square of the same area.
• 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.
• Hypotenuse - RT A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area 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.
• Proof PT Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.
• 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.
• Euclid1 Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
• Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
• Area of RT In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
• 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.
• Sides of the triangle Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
• 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?

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