# Expression of a variable from the formula + right triangle - math problems

#### Number of problems found: 280

- Trip with compass

During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip? - Integer sides

A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - 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. - 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´? - Perimeter and diagonal

The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Height of pyramid

The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - The tent

Calculate how much cover (without a floor) is used to make a tent that has the shape of a regular square pyramid. The edge of the base is 3 m long and the height of the tent is 2 m. - Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. - 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? - 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? - 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. - 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. - Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - 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? - 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: - 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. - Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - 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).

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