Pythagorean theorem - math word problems

Number of problems found: 701

Perpendicular projection
Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
Ladder
How long is a ladder that touches on a wall 4 meters high and its lower part is 3 meters away from the wall?
Railway embankment
The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
The pyramid
The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid.
Isosceles triangle
Calculate the area of an isosceles triangle, the base of which measures 16 cm and the arms 10 cm.
Right triangle
A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees.
Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
Find the 13
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
Calculate 6
Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
Sailing
Solve the following problem graphically. The fishing boat left the harbor early in the morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then When she docked and reached the fishing grounds she launched
Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
The right triangle
In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.
Diamond area from diagonals
In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.