9th grade (14y) + The right triangle altitude theorem - examples
- Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
- Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
- Area of RT
Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
- Rhombus and inscribed circle
It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals.
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 ?.
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.
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
- 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.
- 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.
- Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
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 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 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.
- 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 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?
- 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.