Right triangle + system of equations - practice problems - page 3 of 4
Number of problems found: 74
- Diagonal 20
The rectangular town plaza's diagonal pathway is 20 m longer than the width. Suppose the pathway is 20 m shorter than twice the width. How long should the pathway be? - Circumference 5254
Calculate the shorter side and the diagonal of the rectangle if one side is 2 cm longer than the other and its circumference is equal to 70 centimeters. - Circumference 7615
The sides of the rectangle are in a ratio of 3:5. Its circumference is 48 cm. Calculate the length of its diagonal. - Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Railway embankment
The railway embankment section is an isosceles trapezoid, and the bases' sizes are in the ratio of 5:3. The arms have a length of 5 m, and the embankment height is 4.8 m. Calculates the size of the embankment section area. - Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are at a ratio of 5:3. The arm is 6cm long and 4cm high. - Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle. - X-coordinate 81737
In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Intersection 5413
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Six-sided polygon
There is a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle. - Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - One-third 77724
The cuboid has a body diagonal u=25 cm, and side b is one-third longer than side a. What is the volume of the cuboid?
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