# Math Solving Problems With Answers

In the right triangle ABC, the side which is opposite to angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

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A balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 degree angle . (Imagine that there is no slack in the cable) Here, AB represents height of the building, BC represents distance of the building from the point of observation.

In the right triangle ABC, the side which is opposite to the angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Solution: Let x be the amount of milk the first cow produced during the first year.

Then the second cow produced $(8100 - x)$ litres of milk that year.

At the same moment, a passenger car and a truck start moving towards each other from different towns. If the car drives 5 km/hr faster than the truck, what are their speeds?

Problem 9The first year, two cows produced 8100 litres of milk.Then she has $x-\frac\cdot x=\frac\cdot x$ pages left.$\frac\cdot x-\frac\cdot x=90$ $\frac\cdot x=90$ $x=270$So the book is 270 pages long.Now we need to find the length of the side AB.tanθ = Opposite side/Adjacent sidetan 60° = AB/BC√3 = AB/50√3 x 50 = ABAB = 50√3Approximate value of √3 is 1.732AB = 50 (1.732) AB = 86.6 m So, the height of the building is 86.6 m.Here AB represents height of the wall, BC represents the distance between the wall and the foot of the ladder and AC represents the length of the ladder.The second year their production increased by 15% and 10% respectively, and the total amount of milk increased to 9100 litres a year.How many litres were milked from each cow each year?Here AB represents height of the tower, BC represents the distance between foot of the tower and the foot of the tree.Now we need to find the distance between foot of the tower and the foot of the tree (BC)θ = Opposite side/Adjacent sidetan 30° = AB/BC1/√3 = 30/BCBC = 30√3 Here BC represents height of the light house, AB represents the distance between the light house from the point of observation.If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days.How many hectares a day would one tractor plough then?

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