Cotangent - practice for 14 year olds
Number of problems found: 23
- One side 4
One side of a regular octagon is 12 inches. Find the apothem and its area. - Isosceles 81130
The angle at the apex of an isosceles triangle is 78°. Base 28.5cm. Shoulder length? - A hiker
A hiker plans to hike up one side of a mountain and down the other side of points a mountain, each side of the mountain formed by a straight line. The angle of elevation at the starting point is 42.4 degrees, and the angle of elevation at the end is 48.3 - Three pillars
On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Vlado see each pillar if it is 30 m from the first and his eyes are 1.8 m high?
- Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - 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). - 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°. - The ladder
The ladder touches a wall at the 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? - Observation tower
The observation tower has a height of 105 m above sea level. The ship is aimed at a depth angle of 1° 49' from the tower. How far is the ship from the base of the tower?
- Perpendicular 17423
According to the map, the scouts were supposed to proceed through the forest perpendicular to its straight edge, where the goal was 3 km away from the starting point. They already deviated from the correct direction by 5° at the start. How far from the ta - 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. - 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'. - Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - Measurements 8129
The plane flies at an altitude of 22.5 km to the observatory. At the time of the first measurement, it was seen at an elevation angle of 28° and during the second measurement at an elevation angle of 50°. Calculate the distance it flies between these two
- KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees. - Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Tree
Between points A and B is 50m. From A, we see a tree at an angle of 18°. From point B, we see the tree at a three times bigger angle. How tall is a tree? - 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) - 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.
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