# Angle + expression of a variable from the formula - math problems

#### Number of problems found: 113

- 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´? - Digging a pit

The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m^{3}of soil were excavated when digging the pit? - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - Tangents to ellipse

Find the magnitude of the angle at which the ellipse x^{2}+ 5 y^{2}= 5 is visible from the point P[5, 1] . - 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). - Fighter

A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h. - Diagonal BD

Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42° - 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. - 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 ’? - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - 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 from median

Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5. - 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. - TV tower

Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°? - Parallelogram

Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Quadrilateral pyramid

The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - The angles ratio

The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is.

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.