Expression of a variable from the formula + Pythagorean theorem - practice problems - page 10 of 29
Number of problems found: 576
- Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Equilateral cone
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? - Isosceles 27793
The LICH isosceles trapezoid has 5.2 cm long arms and its bases are 7.6 cm and 3.6 cm long. Find the area of the LICH trapezoid. - 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. - Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. - Calculate 27441
Calculate the length of the side of the square if the size of the diagonal u = 9.9 cm is entered. - Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge 12 cm long and the side edge 20 cm. - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - Calculate 26991
How can you calculate the wall height of a pyramid when you know: the length of the base edge: is 28 mm and: the body height: is 42 mm? - 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? - 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? - Motorcyclist 26141
The passenger car left at 7:00 and was heading east at a speed of 60km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock? - Horizontal 26131
What height difference does the 2.5 km long ski lift overcome when the horizontal distance of the entry and exit station is 1200 meters? - Sidewalk 26121
The garden has a square shape, and its area is 8,100 m². It will be divided by a sidewalk connecting the two opposite garden peaks. How long will this trail be? - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - 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.
- Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Sailing
Solve the following problem graphically. The fishing boat left the harbor early 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 the ne - 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.
- Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
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