Triangle - 9th grade (14y) - examples - page 7
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In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
- Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
- The cone
The lateral surface area of the cone is 4 cm2, the area of the base of the cone is 2 cm2. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci
- Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 71 cm) is 27 cm?
- Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 15 cm, 15 cm, 8 cm.
- Trapezoid ABCD v2
Trapezoid ABCD has length of bases in ratio 3:2. The area of riangle ACD is 956 dm2. What is the area of trapezoid ABCD?
- Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
- Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
- Angles in triangle
The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle?
- Angle of deviation
The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
On each side of the square is marked 2 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
- Angles ratio
In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
- Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
- SAS triangle
The triangle has two sides long 7 and 19 and included angle 144°11'59″. Calculate area of this triangle.
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
The longer leg of a 30°-60°-90° triangle measures 7. What is the length of the shorter leg?
- Field with vegetables
Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
- Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
- Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
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