Cosine + expression of a variable from the formula - practice problems - page 3 of 5
Number of problems found: 85
- 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. - Magnitude 25411
There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord. - Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
- Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Triangle from median
Calculate the perimeter, area, and magnitudes of the triangle ABC's remaining angles: a = 8.4; β = 105° 35 '; and median ta = 12.5. - The bases
The bases of the isosceles trapezoid ABCD have 10 cm and 6 cm lengths. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and area of the ABCD trapezoid. - Two groves
Two groves A B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'? - Trapezoid: 18703
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle.
- Power line pole
From point A, the power pole is visible at an angle of 18 degrees. From place B, which we reach if we go from place A 30m towards the pillar at an angle of 10 degrees. Find the height of the power pole. - The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considere - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - The aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - A rhombus
A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
- Isosceles triangle 10
In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles. - Roof angle
The house's roof has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make? - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Described 7872
In the KLM isosceles triangle, the KL base is 24 cm long, and the arm measures 15 cm. What is the radius of the circle described by this triangle? - Children playground
The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles.
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