Question

a pilot in an apache rescue helicopter at an altitude of 1200 feet,spots his two soldiers on the ground. The angles of depression to the soldiers are 53 and 30. How far apart are the two soldiers to the nearest foot. PLEASE HELP ASAP I NEED IT NOW!!!!!!!!

Answer 1

The distance between the soldiers is 1174 ft.

Explanation:

See the attached diagram.

Let the position of the pilot is at B and AB = 1200 ft.

Now, the first soldier is at C and the second one is at D.

Therefore, ∠ BCA = 53° and ∠ BDA = 30°.

{Since angle of depression from pilot to the soldier is equal to the angle of elevation from soldier to pilot.}

Now, from the Δ ABC,

`\tan 53 ^(\circ) = (AB)/(AC) = (1200)/(AC)`

⇒ AC = 904.265 feet.

Again, from Δ ABD,

`\tan 30 ^(\circ) = (AB)/(AD) = (1200)/(AD)`

⇒ AD = 2078.461 feet.

So, the distance between the soldiers = CD = AD - AC = 2078.461 - 904.265 = 1174 feet (Approx.) (Answer)