Tangent - practice problems - page 6 of 16
Number of problems found: 303
- Tower's view
From the church tower's view at 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the house's height and its distance from the church.
- Aircraft
From the aircraft flying at an altitude of 500m, they observed places A and B (at the same altitude) in the direction of flight at depth angles alpha = 48° and beta = 35°. What is the distance between places A and B?
- Altitude angle
In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we saw it at an altitude angle of 25°?
- Calculate 43331
From the lookout tower, 70 meters high, we see a man at a depth angle of 15 degrees. Calculate how far one stands from the base of the lookout tower. Draw and calculate.
- Inclination 43321
What percentage of the gradient should be indicated on the mark if the angle of inclination of the road is 6 ° 25'?
- Base diagonal
In a regular four-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 pyramid's surface area and volume.
- Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
- 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.
- The body
The body slides down an inclined plane, forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s². At what angle β must the plane be inclined so that the body slides on it af
- Tangens parallelogram
If ∠BAD between the sides AB and AD of the parallelogram is θ, what is tan θ? See diagram: A=(7,1) B=(5,-2) C=(12,1) D=(14,4)
- Tourist 39691
How far from the lookout tower, 48 m high, did the tourist stand if he saw its top at an angle of 40°?
- Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
- Ratio in trapezium
The ratio of the height v and the base a, c in the trapezoid ABCD is 1:6:3. Its area is 324 square cm, and the peak angle B is 35 degrees. Determine the perimeter of the trapezoid.
- Calculate pyramid
Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60° with the square base.
- Nine-sided 36071
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm
- The staircase
The staircase has a total height of 3.6 m and forms an angle of 26° with the horizontal. Calculate the length of the whole staircase.
- 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.
- Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
- Calculate cone
The rotating cone has a base radius r = 226 mm, and the deviation of the side from the base plane is 56°. Calculate the height of the cone.
- The tangent line
Find the tangent line of the ellipse 9x² + 16y² = 144 with slope k = -1.
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