Practice problems of the right triangle - page 27 of 81
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1619
- Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle? - Right-angled triangle
Determine the area of a right triangle whose side lengths form successive members of an arithmetic progression, and the radius of the circle described by the triangle is 5 cm. - EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=77 cm. - Rectangle 62854
The aspect ratio of the rectangle and its diagonal is 9:12:15. Calculate the area of the rectangle if the length of the diagonal is 105 cm. - Equilateral 5140
I have a circle with a diameter of 6.4 cm. I need to find out the length of the side of an equilateral triangle inscribed in a circle. - Circumscribed 3132
The right triangle has squares in the ratio of 5:12, and the circumscribed circle diameter is 26 cm. Determine its perimeter. - Crossroads
A passenger car and an ambulance come to the rectangular crossroad, and the ambulance leaves. Passenger car at speed 39 km/h and ambulance at 41 km/h. Calculate the relative speed of the ambulance moving to the car. - Side and diagonal
Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm. - Meridian ground speed
The plane flies south at an average speed of 190 km/h, and the wind blows from west to east at a speed of 20 m/s. How fast and in what direction (relative to the meridian) will the plane move relative to the ground? - Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the identical chocolate roller of a prism shape with a length of 0.5 m whose cross-section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm? You know that 100 g of - Rotating 28501
Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm. - Billboard
A rectangular billboard is 2.5 m long with a diagonal of 2.8 m long. Calculate the perimeter and the area of the billboard. - Perimeter 6254
Perimeter and area of the rectangle. Diagonal 260m and one side 150m - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - Reverse Pythagorean theorem
Given are the lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ... Δ DEF: 55 dm, 82 dm, 61 dm ... Δ GHI: 24 mm, 25 mm, 7 mm ... Δ JKL: 32 dm, 51 dm, 82 dm ... Δ MNO: 51 dm, 45 - Diagonal to area
Calculate the area of a rectangle in which the diagonal length is 10 cm. - Acreage
What acreage has a rectangular plot whose diagonal is 34 meters long, and one side has a length of 16 meters? ... - Triangle
Calculate the area of the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius). - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Dimensions: 32561
The convex lens consists of two spherical segments (dimensions given in mm). Calculate its weight if the density of the glass is 2.5 g/cm³. Dimensions: 60mm in length and width of the upper part 5mm, the width of the lower part 8mm
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