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

- 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°? - The ladder

The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall? - Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - 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´? - 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. - 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? - Side lengths

In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower? - 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. - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - The right triangle

The right triangle ABC has a leg a = 36 cm and an area S = 540 cm^{2}. Calculate the length of the leg b and the median t2 to side b. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - In a

In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides. - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - 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. - Spherical cap

The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - A kite

Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain? - Height to the base

The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base. - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

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See also our trigonometric triangle calculator. See also more information on Wikipedia.