# Examples for 9th grade - page 6

- Right triangle

Legs of right are in ratio a:b = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle. - Mast

Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm. - Rectangle

Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees. - Radians

Convert 54° to radians. Write result as multiple of number π. - Railways

Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters. - Ravens

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 1.5 years after the previous one. When the eldest of the brothers was 4-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - Rectangle

In rectangle ABCD with sides |AB|=11, |AD|=12 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 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg. - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Sand pile

Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c - Tangents

To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre. - Car

Car goes from point A to point B at speed 70 km/h and back 76 km/h. If they goes there and back at speed 73 km/h trip would take 19 minutes shorter. What is distance between points A and B? - Lathe

From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - Described

Calculate perimeter of the circle described by a triangle with sides 418, 59, 430. - Barrel of oil

Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - VAT

John paid 1000 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%.

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