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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