Tangent + Pythagorean theorem - practice problems - page 2 of 4
Number of problems found: 68
- Rhombus
One angle of a rhombus is 136°, and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - Right triangle
It is given a right triangle angle alpha of 90 degrees the beta angle of 55 degrees c = 10 cm use the Pythagorean theorem to calculate sides a and b - Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees. - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - Quadrilateral 5112
The body diagonal of a regular quadrilateral prism forms an angle of 60 ° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - River
From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river. - 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). - Calculate 8354
In a regular pyramid in which the edge of the base is | AB | = 4cm; height = 6cm, calculate the angle of the lines AV and CV, V = vertex. - Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60°, and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Climb
The road sign which informs the climb is 8.7%—the car drive 5 km along this road. What is the height difference that the car went? - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Embankment 7879
An embankment 7.5 m high should be built on the horizontal plane. The width of the upper surface of the embankment is 2.9 m, and the slope is 35 °. What will be the lower width of the embankment? - An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side. - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%. - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Determine 83083
A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall.
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