Equation + triangle - practice problems - page 2 of 15
Number of problems found: 288
- Perpendicular 81837
Two neighboring cottagers have cottages under the forest by the stream. They decided to build a bridge over the stream at a place far from the two huts. The distance between the cottages is 230 m; one cottage is 120 m from the stream, and the other is 85 - 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. - Determine 81708
The perimeter of the triangle is 110 cm. Side a is 6 cm longer than side b and 8 cm shorter than side c. Determine the lengths of the sides of the triangle. - Coefficient 81704
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - Intersection 81611
Given a triangle ABC: A (-1,3), B(2,-2), C(-4,-3). Determine the coordinates of the intersection of the heights and the coordinates of the intersection of the axes of the sides. - Intersection 81594
Given a trapezoid ABCD and the sizes of the interior angles. Angle SDC 32° SAD angle 33° SDA angle 77° Angle CBS 29°, where S is the intersection of the diagonals. What is the size of the angle BSA? - Determine 81572
In one triangle, one angle is 43°, and the second is 15° less than the third. Determine the unknown angles of the triangle. - Complementary 81152
In a certain polygon, the ratio of the sum of the sizes of its internal angles and the sum of the sizes of the complementary angles is 2:5. How many vertices does this polygon have? - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Circle's 81078
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - 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. - Determine 79364
Given a general triangle ABC. Its perimeter is 30 cm, with side a=2 cm longer than side b and 5 cm shorter than side c. Determine the area of the triangle. - 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. - Quadrilateral 78874
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime - Calculate 78714
Calculate the size of the base and side of an isosceles triangle if the side is 1 cm longer than the base and the height to the base is 2 cm shorter than the side. - Opposite 78434
We see the tree on the opposite bank of the river at an angle of 15° from a distance of 41m from the river bank. From the bank of the river, we can see at an angle of 31°. How tall is the tree? - 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? - Angles in a triangle
In a triangle, the first angle measures a number plus 45°, and the second angle is 30° less than the first angle. The third angle is two times the number more than the first angle. What are the measurements of each angle of the triangle? - Find all
Find all right-angled triangles whose side lengths form an arithmetic sequence. - Regular polygons
Two regular polygons, x and y, are such that the number of sides of x is three more than the number of the sides of y. If the sum of the exterior angles of x and y is 117°, how many sides have x?
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