A flagpole stands on a building of height 450 ft and an observer at 300 ft above the ground level. And if angle of elevation of the bottom of the flagpole is 30° and that of top is θ. Also if hight the flagpole is 50 ft such that tan θ is equal to ( p / q √3), then find the value of ( q / p ).

Question

A flagpole stands on a building of height 450 ft and an observer at 300 ft above the ground level. And if angle of elevation of the bottom of the flagpole is 30° and that of top is θ. Also if hight the flagpole is 50 ft such that tan θ is equal to ( p / q √3), then find the value of ( q / p ). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

In triangle DCE, tan 30°=(150/ CD ) ⇒ CD =√3 × 150 Now, in triangle DCF, tan θ=( DF / CD )=(200/√3 ⋅ 150)=(4/3 √3) So q / p=3 / 4=0.75

Q. A flagpole stands on a building of height 450ft and an observer at 300ft above the ground level. And if angle of elevation of the bottom of the flagpole is 30∘ and that of top is θ. Also if hight the flagpole is 50ft such that tanθ is equal to q3​p​, then find the value of pq​.

In △DCE, tan30∘=CD150​ ⇒CD=3​×150 Now, in △DCF, tanθ=CDDF​=3​⋅150200​=33​4​ So q/p=3/4=0.75

In $△ D CE$ ,
$tan 3 0^{\circ} = \frac{150}{C D}$
$\Rightarrow C D = 3 \times 150$
Now, in $△ D CF$ ,
$tan θ = \frac{D F}{C D} = \frac{200}{3 \cdot 150} = \frac{4}{3 3}$
So $q / p = 3/4 = 0.75$