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6. A tower subtends an angle α at a point A in the place of its base and the angle of depression of the foot of the tower at a point b ft. just above A is β. Prove that the height of the tower is b tan α cot β. read less

Let CD is the height of the tower. ie, C is the bottom of the tower.

Let AB is b ft. 

in trinagle ABC,

          (1)

In triangle ACD,

        (2)

From (1) and (2)/

therefore, 

 

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2. A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? read less

3. There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are the points directly opposite to each other on the two banks, and in a line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find the height of the tree. read less

First 10 Natural numbers are:- 1,2,3,4,5,6,7,8,9,10

Mean = Sum of all numbers/ total number of observations

        = 1+2+3+4+5+6+7+8+9+10 / 10 

        = 55/ 10 

        = 5.5

Therefore, 5.5 is the mean of first 10 natural numbers

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6.If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18, 1, a, b is 50. What is the value of b? read less

in this question mean is already given and we know that:-

           mean = sum of total numbers / total number of observations

             15 = 2+6+7+a / 4

             15*4 = 15+a

               60 = 15+a

               60-15 = a

                 a= 45

now we have found the value of a=45, we will put this value in second series:-

                mean = sum of all numbers / total number of observations

                50 = 6+18+1+45(value of a) + b / 5

                50*5 = 70 + b

                250 = 70 + b

                 b = 250 - 70

                 b = 180

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10. Construct a ΔABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm. read less

2. If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, calculate the circumference (in cm) of the circle. read less

3. While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. Find the correct mean. read less