# Find The Height of The Aeroplane Above The Ground

From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30 degree and 45 degree. The height of the aeroplane above the ground is :

- 10√3 m
- 10(√3 -1 ) m
- 10 (√3 +1) m
- 20 m

**Answer: (3) 10 (√3 +1) m**

**Explanation:-**

Let be the height of the plane = h m

**In the figure-**

Tan30^{o} = h/X + 201/sqrt.3 = h/(X + 20)

X + 20 = h sqrt.3

X = h sqrt.3 – 20 …………….. (1)

Tan45^{o} = h/X

1 = h/X

X = h ………………………………………. (2)

Comparing equation (1) & (2)

h = h sqrt.3 – 20

h – h sqrt.3 = – 20

h (sqrt.3 – 1) = 20

h = 20/(sqrt.3 – 1)

= 20 (sqrt.3 + 1)/(sqrt.3 – 1) (sqrt.3 + 1)

= 20 (sqrt.3 + 1)/(sqrt.3)^{2} – 1^{2}

= 20 (sqrt.3 + 1)/3 – 1

= 20 (sqrt.3 + 1)/2

= 10 (sqrt.3 + 1) m

Hence, the answer is (3) 10 (sqrt.3 + 1) m.