That is, we have to find the length of θ = Opposite side/Adjacent sidetan60° = AB/BC√3 = 6/BCBC = 6/√3BC = (6/√3) x (√3/√3)BC = (6√3)/3BC = 2√3Approximate value of √3 is 1.732BC = 2 (1.732)BC = 3.464 m Here AB represents height of kite from the ground, BC represents the distance of kite 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?
sin θ = Opposite side/Hypotenuse side sin θ = AB/ACsin 60° = AB/200√3/2 = AB/200AB = (√3/2) x 200AB = 100√3Approximate value of √3 is 1.732AB = 100 (1.732)AB = 173.2 m So, the height of the balloon from the ground is 173.2 m.
Problem 1 A salesman sold twice as much pears in the afternoon than in the morning. Then Mary and Lucy picked $2x$ and $x 2$, respectively.
Therefore in 5 days they ploughed $5 \cdot 4 \cdot x = 20 \cdot x$ hectares, which equals the area of the whole field, 2880 hectares. Hence, each of the four tractors would plough 144 hectares a day.
Problem 7 The distance between two towns is 380 km.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).Problem 4A farming field can be ploughed by 6 tractors in 4 days.When 6 tractors work together, each of them ploughs 120 hectares a day.Here AB represents height of the wall, BC represents the distance of the wall from the foot of the ladder.In the right triangle ABC the side which is opposite to the angle 20 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). Cos θ = Adjacent side/Hypotenuse side Cos θ = BC/ACCos 20° = 3/AC0.9396 = 3/ACAC = 3/0.9396AC = 3.192So, the length of the ladder is 3.192 m. In the right triangle ABC the side which is opposite to angle 31 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). Sin θ = Opposite side/Hypotenuse side Sin θ = AB/ACSin 31° = AB/AC0.5150 = 65/ACAC = 65/0.5150AC = 126.2 m Hence, the length of the string is 126.2 m.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.If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon? This must be equal to 360.x = 360$$x = \frac$$x = 120$ Therefore, the salesman sold 120 kg in the morning and \cdot 120 = 240$ kg in the afternoon. Together the three of them picked 26 kg of chestnuts. So $x 2x x 2=26$x=24$$x=6$ Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.Solution: Let $x$ be the number of kilograms he sold in the morning. Problem 2 Mary, Peter, and Lucy were picking chestnuts. Solution: Let $x$ be the total number of pages in the book, then she finished $\frac\cdot x$ pages.