# Examples for secondary school students - page 45

- Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ) - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - Three dice

When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice? - Cubes - diff

Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm^{3}. Calculate the sizes of the edges of the two dice. - Log

Calculate value of expression log |3 +7i +5i^{2}| . - Book

Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book? - Debt

Joe and Caryl have a debt of $100,500. Joe makes $90,000 per year, and Caryl makes $35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries? - Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - The city

At the end of 2010 the city had 155000 residents. The population increased by 2.1% each year. What is the population at the end of 2013? - Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point. - Water reservoir

The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one. - Diamond

Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - Class - boys and girls

In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl? - Car and cyclist

Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car? - Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120° - Enterprise

The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 1.5%. What will be value of production at the end of the fifth year? - Medians and sides

Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6). - Wavelength

Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s. - Bank

Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%. - Interesting property

Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?

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