Question

the elevation of a tower at a station A due north of it is alpha and at station B due west of A is beta. prove that the ... AB sin alpha sine beta/ root sin²alpha - sin²beta​

Answer 1

Let O be the point where the tower stands.

Let A be the point due north of it and B the point due east of A.

From A the angle of elevation of the tower is α.

∴ OA / h = cot α ⇒ OA = h Cot α ----------→(1)

From B the angle of elevation of the tower is β.

∴Cot β = OB / h ⇒ OB = h cot β -------------→(2)

Consider ΔOAB

AB2 = OB2 - OA2

= h2 Cot2 β - h2 cot2 α

=h2 (Cos2 β / Sin2 β- Cos2 α / Sin2 α)

=h2 (Sin2 α Cos2 β - Cos2 α Sin2 β) / Sin2 α Sin2 β.

=h2 (Sin2 α (1-Sin2 β) - (1-Sin2 α) Sin2 β) / Sin2 α Sin2 β.

AB2 =h2 (Sin2 α - Sin2 β) / Sin2 α Sin2 β.

h2 = AB2 Sin2 α Sin2 β./ (Sin2 α - Sin2 β)

∴ h = AB Sin α Sin β./ √(Sin2 α - Sin2 β).

hope this answer helpful u

Answer 2

Answer:

Step-by-step explanation: