Angle + tangent - practice problems - page 5 of 13
Number of problems found: 242
- 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. - Trigonometric formula
Determine the value of the function tg x (tangens) when cotg x = -0.8 (cotangent); x holds in the second quadrant) - 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'. - 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 - 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. - 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 - Angle
A straight line p given by the equation y = (-8)/(6) x +78. Calculate the size of the angle in degrees between line p and y-axis. - 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. - 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 - 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 - 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. - Fighter
A military fighter flies at an altitude of 10 km. The ground position 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. - Difference 83079
On the traffic sign that informs about the road's gradient, the figure is 6.7%. Determine the slope angle of the path. What height difference is covered by the car that traveled 2.8 km on this road? - A construction
A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an angle of elevation of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find - 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. - Angle of cone
The cone has a base diameter of 1.5 m. The angle at the central apex of the axial section is 86°. Calculate the volume of the cone.
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