# Which Gives The Best Approximation to The Height of The Tower?

A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3m. From a point on the field, the angles of elevation of the bottom and tip of the flag staff are 30o and 45o respectively. Which one of the following gives the best approximation to the height of the tower?

1. 3.90 m
2. 4.00 m
3. 4.10 m
4. 4.25 m
Anurag Mishra Professor Asked on 3rd October 2015 in

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Answer; (3) 4. 10 m

Explanation:-

In the figure-

Let AB = h metres and DA = X meters
Then, In Triangle ABD ,
tan 30 degree = AB/AD
1/sqrt.3 = h/X
X = h sqrt.3                   ……………………… (1)

Again, in Triangle ADC,
tan 45 degree = AC/AD
AC = AD tan 45 degree
h + 3 = AD
h + 3 = X          …………………………………………. (2)
Comparing equation (1) & (2),
Then, h sqrt. 3 = h + 3
h sqrt. 3 – h = 3
h (sqrt. 3 – 1) = 3
h = 3/(sqrt. 3 – 1)
h = 3 (sqrt.3 + 1)/(sqrt. 3 – 1) (sqrt.3 + 1)
h = 3 (sqrt. 3 + 1)/(3 – 1)
h = 3 (1.732 + 1)/2
h = 1.5 x 2.732
h = 4.098 or 4.10 (approximately)

Hence, the answer is (3) 4.10 m

Anurag Mishra Professor Answered on 3rd October 2015.