Triangle + tangent - practice problems - page 5 of 13
Number of problems found: 257
- Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Trigonometric formula
Determine the value of the function tg x (tangens) when cotg x = -0.8 (cotangent); x holds in the second quadrant) - EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=77 cm. - Circles
Three circles of radius 30 cm, 28 cm, and 37 cm are mutually tangent. What is the triangle perimeter whose vertices are the circles' centers? - Inscribed 3689
There is a triangle ABC whose perimeter is 2s (2s = a + b + c), and the circle k (S, ρ) is the inscribed circle of the triangle. Calculate the length of the tangent of the circle k from point A. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm, and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - 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 - Directional 2595
Calculate the interior angles of triangle ABC using vectors. Coordinates A [2; 4] B [4; 6] C [0; -4]. Calculate directional vectors of sides, parametric and general equations of sides, parametric and general equations of lines, calculate area, calculate h - 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. - Elevation 80869
We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tow - Slope of the pool
Calculate the slope (rise:run) of the bottom of the swimming pool long 10 m. The water depth at the beginning of the pool is 0.96 m (for children), and the depth at the end is 1.86 m (for swimmers). Slope express as a percentage and as the angle in degree - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Determine 8202
An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane. - The chimney
How high is the chimney if we see it from a distance of 60 m at an angle of 42°? - Map - climb
On the map of the High Tatras, on a scale of 1:11000, are cable car stations in the Tatranska Lomnica and the Skalnate Pleso with a distance of 354.6 mm. The altitude of these stations is 949 m and 1760 m. What is the average angle of climb on this cable - Calculate 3019
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Calculate 83261
Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the top A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3
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