The right triangle altitude theorem - practice problems - last page

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: 56

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.
RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
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.
Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
MIT 1869
You know the length of hypotenuse parts 9 and 16, at which the hypotenuse of a right triangle is divided by a perpendicular running from its opposite vertex. The task is to find the lengths of the sides of the triangle and the length of the line x. This a
Paratrooper
After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity concerning the ground, b) the distance of his land from a
The bomber
From what distance in front of the target must a parachute load be dropped from an aircraft flying at an altitude of 1260 m if it slopes at a speed of 5.6 m/s and at the same time is carried in the direction of movement at a speed of 12 m/s. What is the d
An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
Touch circle
Point A has a distance IA, kl = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l
Construct 47633
Construct a square that has the area as a rhombus ABCD ak / AB / = 5cm, / AD / = 4cm and angle | DAB | = 30 °
Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle).
Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
Same area
There is a given triangle. Construct a square of the same area.
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.

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