Pythagorean theorem + similarity of triangles - practice problems
Number of problems found: 24
- 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. - Intersection 6653
Two straight paths cross, making an angle alpha = 53 degrees 30'. There are two pillars on one of them, one at the intersection, the other at a distance of 500m from it. How far does one have to go from the intersection along the other road to see both po - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl
- Find all
Find all right-angled triangles whose side lengths form an arithmetic sequence. - Reverse Pythagorean theorem
Given are the lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 66 dm, 60 dm, 23 dm ... Δ DEF: 20 mm, 15 mm, 25 mm ... Δ GHI: 16 cm, 20 cm, 12 cm ... Δ JKL: 58 cm, 63 cm, 23 cm ... Δ MNO: 115 mm, - Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went? - 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? - Right-angled triangle
The right-angled triangle XYZ is similar to the triangle ABC, which has a right angle at the vertex X. The following applies: side a = 9 cm, x=4 cm, x = v-4 (v = height of triangle ABC). Calculate the unknown side lengths of both triangles.
- TV diagonal
A diagonal TV is 0.56 m long. How big is the television screen if the aspect ratio is 16:9? - Right-angled 80745
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Isosceles 6673
Isosceles triangle X'Y'Z' . It is similar to triangle XYZ. The base of triangle XYZ has length |XY|=4cm. The size of the angle at the X vertex is 45 degrees. Draw a triangle X'Y'Z' whose base is 8 cm long. - Area of iso-trap
Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm and the diagonals are perpendicular to each other.
- Triangle KLB
It is given an equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percent of the area of the triangle AB - Railways
Railways climb 2.8 ‰. Calculate the height difference between two points on the railway distant 5997 meters. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - Calculate 7214
Two tangents are drawn from point C to a circle with a radius of 76 mm. The distance between the two contact points is 14 mm. Calculate the distance of point C from the center of the circle.
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?Do you have unsolved problem that you need help? Ask a question, and we will try to solve it. Solving math problems.
