# Cotangent - math problems

In a right triangle, the cotangent is defined as the ratio of the adjacent perpendicular to the opposite perpendicular. It is the reciprocal value of the tangent of a given angle.

#### Number of problems found: 27

• 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 at 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).
• 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.
• 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 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?
• 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?
• The rescue helicopter
The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
• Tetrahedral pyramid 8
Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
• A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at the height of 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in me
• 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.
• Depth angles
At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
• 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.
• Balloon and bridge
From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
• 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?
• Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
• Tree
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in 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)

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