Sine + expression of a variable from the formula - practice problems - page 3 of 5
Number of problems found: 90
- 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. - Pentadecagon
Calculate the area of a regular 15-sides polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Circumference 26361
The ABCD diamond has a circumference of 72 cm. The longer diagonal of the animal with the line segment AB angle is 30 °. Calculate the area of the ABCD diamond. - Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
- 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. - Telegraph poles
The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30’? - 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.
- 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. - 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. - 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.
- ABCDEFGHIJKL 8426
The given is a regular hexagonal prism ABCDEFGHIJKL, which has all edges of the same length. Find the degree of the angle formed by the lines BK and CL in degrees. - 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? - Triangle 8027
Side a in the right triangle has size a = 120 mm, angle A = 60°. How big is the hypotenuse c? - 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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