When the suns altitude changes from 30 degree to 60 degree the length of the shadow of a tower decreases by 70 What is the height of the tower?

When the sun s altitude changes from 30° to 60°, the length of the shadow of a tower decreases by 70m. What is the height of the tower?

Explanation:

Let AD be the tower, BD be the initial shadow and CD be the final shadow.Given that BC = 70 m, $\angle$ABD = 30°, $\angle$ACD = 60°,Let CD = x, AD = hFrom the right $\triangle$ CDA, tan60°=$\dfrac{AD}{CD}$√3=$\dfrac{h}{x} $ ⋯(eq:1)From the right $\triangle$ BDA, tan30°=$\dfrac{AD}{BD}$$\dfrac{1}{\sqrt{3}}=\dfrac{h}{70+x} $ ⋯(eq:2)$\dfrac{eq:1}{eq:2}⇒\dfrac{\sqrt{3}}{\left( \dfrac{1}{\sqrt{3}} \right)}=\dfrac{\left( \dfrac{h}{x}\right)}{\left( \dfrac{h}{70+x}\right)}$⇒3=$\dfrac{70+x}{x}$⇒2x=70⇒x=35Substituting this value of x in eq:1, we have√3=$\dfrac{h}{35}$⇒h=35√3=35×1.73=60.55≈60.6

Next Question

A person, standing exactly midway between two towers, observes the top of the two towers at angle of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower? (Given that tan 22.5° = √2−1)

When the sun's altitude changes from 30∘ to 60∘, the length of the shadow of a tower decreases by 70 m. What is the height of the tower?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Suggest Corrections