A spherical balloon of radius r subtends an angle theta at the eye of an observer. If the angle of elevation of its centre is fye,find the height of the centre of the balloon.
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⛦Hᴇʀᴇ Is Yoᴜʀ Aɴsᴡᴇʀ⚑
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➧ Let the height of centre of the balloon above the ground be h m.
➧ Since the balloon subtends an angle θ at the observes eye,
➾ ∴ ∠EAD = θ
➧ In ∆ ACE and ∆ ACD,
➾ AE = AD
♦ (lengths of tangents drawn from an external point to the circle are equal)
➾ AC = AC (common)
➾ ∠CEA = ∠CDA = 90°
♦ (Radius is perpendicular to tangent at point of contact)
∴ ∆ ACE ≅ ∆ ACD
➾ ∠EAC = ∠DAC ----- (C.P.C.T)
▶ Next Steps (See in Image)...✔
_________
Thanks...✊
▬▬▬▬▬▬▬▬▬▬▬▬☟
➧ Let the height of centre of the balloon above the ground be h m.
➧ Since the balloon subtends an angle θ at the observes eye,
➾ ∴ ∠EAD = θ
➧ In ∆ ACE and ∆ ACD,
➾ AE = AD
♦ (lengths of tangents drawn from an external point to the circle are equal)
➾ AC = AC (common)
➾ ∠CEA = ∠CDA = 90°
♦ (Radius is perpendicular to tangent at point of contact)
∴ ∆ ACE ≅ ∆ ACD
➾ ∠EAC = ∠DAC ----- (C.P.C.T)
▶ Next Steps (See in Image)...✔
_________
Thanks...✊
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