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6. A tower subtends an angle at a point A in the place of its base and the angle of depression of the... read more
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

Jaisna

Maths online tuition for class 5 to 12.

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, read more

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

Let AB is b ft.

in trinagle ABC,

$taneta&space;=\frac{b}{AC}$

$AC=\frac{b}{taneta&space;}$          (1)

In triangle ACD,

$tan\alpha&space;=\frac{CD}{AC}$

$AC=\frac{CD}{tan&space;\alpha}$        (2)

From (1) and (2)/

$\frac{b}{tan&space;eta}&space;=\frac{CD}{tan&space;\alpha}$

therefore, $CD=&space;b*tan\alpha&space;cot&space;eta$

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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... read more
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

Jaisna

Maths online tuition for class 5 to 12.

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3. There is a small island in the middle of a 100 m wide river and a tall tree stands on the island.... read more
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

Jaisna

Maths online tuition for class 5 to 12.

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5. Find the mean of the first 10 natural numbers.

Swati R.

NET JRF qualified and preparing for PhD..

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 read more

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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Swati R.

NET JRF qualified and preparing for PhD..

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... read more

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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1. How many tangents can a circle have?

Rajn Andini Tiwari

Sophomores NIT Bhopal with 2 years of tutoring experience

A circle can have infinite tangents.
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10. Construct a ABC in which AB = 6 cm, A = 30 and B = 60 . Construct another AB C similar to ... read more
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

1. How many shots each having a diameter of 3 cm can be made from a cuboidal lead solid of dimensions 9cm × 11cm × 12cm?

2. If the difference between the circumference and the radius of a circle is 37 cm, then using = 22/7,... read more
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

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3. While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating... read more
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

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