Heights and Distances Practice Test 1

Let CD = h unit be the height of the tower and A and B be the two points on the ground, such that DA = a; DB = b; ∠ DAC = α and ∠ DBC = 90° – α
From right triangle ADC, CD = h = a tan α ...(i)
From right triangle BDC, CD = h = b tan (90° – α) = b cot α ...(ii)
Multiplying equations (i) and (ii), we get
h2=a‌tan‌α.b‌cot‌α
Hence, h=√ab