The right triangle altitude theorem - math word 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: 39

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.
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.
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.
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.
Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
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.
Area of RT
Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
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 ?.
Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
Right Δ
A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height h_c = 4 cm. Determine the length of both trangle legs.
Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_c=3 cm on the hypotenuse c?
Rhombus
It is given a rhombus of side length a = 19 cm. Touch points 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.
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.
Euclid3
Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg c_b = 39 cm.
RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
Circle in rhombus
In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
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 centre.
Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle h_AB to the side AB.

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