UPSC NDA I 2021 Mathematics Solved Paper

Calculation:
Let AB be the tower and let AC and AD be its shadows when the angles of elevation of the sum are 60∘ and 45∘, respectively. Then, ∠ACB=60∘,∠ADB= 45∘,CD=xm
Let AB=5(3+√3)m and AC=y meterIn △ CAB, We have,
tan‌60∘=‌

AB

AC

√3=‌

5(3+√3)

AC

AC=‌

5(3+√3)

√3

On rationalizing, we get
AC=‌

5(3+√3)

√3

×‌

√3

√3

‌‌=‌

5(3√3+3)

3

In △ DAB, We have,
tan‌45∘=‌

AB

AD

1=‌

AB

AD

AB=AD
AD=5(3+√3)
x+y=5(3+√3)
x+‌

5(3√3+3)

3

=5(3+√3)
x=5(3+√3)−‌

5(3√3+3)

3

x=10m