# Right triangle - 9th grade (14y) - examples - page 3

- Slope of track

Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long. - Climb in percentage

The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km. - Right triangle

Legs of right are in ratio a:b = 2:8. Hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle. - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Mast

Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'. - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - Rectangle

In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - Circular pool

The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm. - Kites

Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°? - Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m^{2}of sheet is required to cover the top of the tower if we count 8% of the sheet waste? - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km.

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