Answer the following:

Question

From a plane flying due east at 300 meters above sea level, the angles of depression of two ships sailing due east measure 12⁰ and 7⁰. Which equation can be used to find the horizontal distance, x meters, to be travelled by the plane so that it will be directly above the closer ship?

Choices:

x = (300 tan 12⁰ - 300 tan 7⁰) / (tan 7⁰ tan 12⁰)

x = 300 / tan 12⁰

x = 300 / tan 7⁰

x = 300 / tan 19⁰

x = 300 tan 12⁰

x = 300 tan 7⁰

Answer 1

From a plane flying due east at 300 meters above sea level, the angles of depression of two ships sailing due east measure 12⁰ and 7⁰. Which equation can be used to find the horizontal distance, x meters, to be travelled by the plane so that it will be directly above the closer ship?

Choices: a) x = (300 tan 12⁰ - 300 tan 7⁰) / (tan 7⁰ tan 12⁰), b) x = 300 / tan 12⁰, c) x = 300 / tan 7⁰, d) x = 300 / tan 19⁰, e) x = 300 tan 12⁰, f) x = 300 tan 7⁰

Detailed Solution:

Given/Known: h = 300 meters, <A = 90, <B = θ = 12⁰ , <C = ∝ = 7⁰. AB = x = ??

h/AB = h/x = tan θ ==> x = h / tan θ

x = h / tan θ

x = 300 / tan 12⁰ meters <== Exact Solution ( b) x = 300 / tan 12⁰)

x = 1411.389033 meters <== Approximated Solution