Exam

NTA Abhyas

Year

2020

Subject

Mathematics

Chapter

Heights and Distances

NTA Abhyas 2020 · Mathematics · Heights and Distances

When the elevation of the sun changes from 45 ^ o to 30 ^ o , the...

When the elevation of the sun changes from ${45}^{o}$ to ${30}^{o}$, the shadow of a tower increases by $60$ units, then the height of the tower is

Step-by-step solution

$tan {45}^{o} = \dfrac{h}{a} ⇒ h = a$

$tan {30}^{o} = \dfrac{h}{a + 60} ⇒ h = \dfrac{\left(a + 60\right)}{\sqrt{3}}$

$⇒ \sqrt{3}h = h + 60$

⇒ h = \dfrac{60}{\sqrt{3} - 1} = \dfrac{60 \left(\sqrt{3} +1\right)}{2} = 30 \left(\sqrt{3} +1\right)& units