Question

A hot air balloon is 70 m above the sea. Two buoys A and B are due East of the

balloon.
The angle of depression from the balloon to buoy A is 60°.
The angle of depression from the balloon to buoy B is 40°.
Calculate the distance AB. (Round to the nearest tenth.)

Answer 1

Explanation:

in the rough drawing i've included we want to find the distance of AC and BC and the subtract the shorter from the longer or

BC- AC = AB

does this strategy seem like a good one?

use the mnemonic SOH CAH TOA to remember how sin, cos, and tan, fit on a triangle

SOH Sin = Opp / Hyp

CAH Cos =Adj / Hyp

TOA Tan = Opp / Adj

where Opp = Opposite side, Adj = Adjacent side , and Hyp = Hypotenuse

we are given an angle and the Opposite side so we can use Tan , since that has the thing we want to find, and the things we know.

when AC is the Adj side it's

Tan(60) = 70 / Adj

Adj = 70 / Tan(60)

Adj = 40.4145

Dist. of AC = 40.4145 m

When BC is the Adj side it's

Tan(40) = 70 / Adj

Adj = 70/ Tan(40)

Adj = 83.42275

Dist. of BC = 83.42275

BC - AC = AB

83.45575 - 40.4145 =43.008

to the nearest tenth AB = 43.0 m