Triangle - math word problems

Triangle
Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
Combi-triangle
On each side of the square is marked 10 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?
30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
Trapezoid ABCD v2
Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm². What is the area of trapezoid ABCD?
Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
Semicircle
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
Cable car 2
Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
The bridge
Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m² of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m² is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.
Shooter
The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?