Right triangle + expression of a variable from the formula - math problems
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.
- 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?
- 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.
- Quadrilateral pyramid
Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
- 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?
- The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. 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?
- 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.
- 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?
- 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?
- Height of the cuboid
Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
- 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 ’?
- Medians in RT
The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
- Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
- Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
- Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
See also our right triangle calculator.