# Examples for 9th grade - page 86

- Lighthouse

The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - Hypotenuse - RT

A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - Children

The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group? - Percentages 5

$5.25 is 7 1/2% of what number? - Paul earned

Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t - Road

The angle of a straight road is approximately 12 degrees. Determine the percentage of this road. - Digit sum

The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number? - Windbreak

A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree? - Inscribed sphere

How many percents of the cube volume takes the sphere inscribed into it? - Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F. - Scale factor

A prism with a volume of 1458 mm^{3}is scaled down to a volume of 16mm^{3}. What is the scale factor in fraction form? - Soaps

Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma - Ratio of sides

The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm. - A square

A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal. - Garden fence

The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced? - Equation with abs

Solve this equation with absolute value member: ? - Tea mixture

Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed? - Distance of numbers

Which number has the same distance from the numbers -5.65 and 7.25 on the numerical axis?

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