Triangle - math word problems

Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
In a
In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
Flakes
A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
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.
Annulus from triangle
Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
The angles ratio
The angles in the ABC triangle are in the ratio 1: 2: 3. find the sizes of the angles and determine what kind of a triangle it is.
The triangles
The triangles KLM and ABC are given, which are similar to each other. Calculate the lengths of the remaining sides of the triangle KLM, if the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5
The conical
The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
Cone roof
How many m² of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
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?
Wall and body diagonals
The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
Embankment
The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m³ of soil is in the embankment?
Similarity of two triangles
The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0 if not, if yes, find and write the coefficient of a similarity)
Clock hands
Calculate the internal angles of a triangle whose vertices lie on the clock's 2, 6 and 11 hours.
A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
Height to the base
The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base.
RT triangle and height
Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
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.