MAH MBA CET Trigonometry Questions

Let the longer pole to be CD and the shorter pole to be AB.
Angle of depression from C to A i.e. angle YCA is 30 degrees which means that angle CAX = 30 degrees.
Angle of depression from C to B i.e. angle YCB is 60 degrees which means that angle CBD = 60 degrees.
Tan CBD = CD/BD where CD = 54 m.
This gives BD = $$\frac{54}{\sqrt{\ 3}}=18\sqrt{\ 3}$$.
In triangle CAX, Tan CAX = CX / AX where Ax = BD = $$\frac{54}{\sqrt{\ 3}}=18\sqrt{\ 3}$$.
This gives CX = 18 m. XD = CD - CX = 36 m.
Height of the shorter pole i.e. AB is equal to XD and thus the correct answer is Option B.

From A, angle of elevation to C i.e. angle CAX is 60 degrees and from A, angle of depression to D i.e. XAD is 30 degrees.
As AX is parallel to BD, angle BDA = XAD = 30 degrees.
Tan BDA = AB / BD where AB = 100 m.
This gives BD = $$100\sqrt{\ 3}$$ m. AX = BD = $$100\sqrt{\ 3}$$ m.
In triangle CAX, Tan CAX = CX/AX.
This gives CX = 300 m and length of CD becomes XD + CX = AB + CX = 400 m.

Angle of depression i.e. YCA = 45 degrees. This makes the angle of elevation from A to C i.e. CAX to be 45 degrees also.
This means that CX = AX and AX is equal to BD i.e. the horizontal distance between them.
CX becomes 75 m. XD = CD - CX ==> 160 - 75 = 85m.
Height of the first tower i.e. AB is equal to XD and thus the correct answer is Option A.