Tangent + triangle - math problemsTangent is a trigonometric function. In a rectangular triangle, it is the ratio of the opposite and adjacent side to a given internal angle. Algebraically is defined as the ratio of the sine and cosine of a given angle. It is periodic with a period of π = 180 °.
Number of problems found: 118
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm2 (B) 20 cm2 (C) 30.78 cm2 (D) 31.84 cm2 (E) 32.90 cm2
- Find the
Find the content of a regular 12 sided polygon, if its side a = 12 cm.
- The bases
The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
- Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
- 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?
- Black diamond run
Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet.
- 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´.
- A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at a height of 300 m above the plane of ABC. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
- Quadrilateral pyramid
In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
- 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.
- An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.
- The ladder
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?
- Angles of elevation
From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of
- Isosceles triangle 10
In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
- Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
- Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
- 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°?
See also our trigonometric triangle calculator.