Video Transcript
A man ran 24 kilometers down a
straight road. He then turned 139 degrees and ran
a further nine kilometers along another straight road. Find to the nearest kilometer the
shortest distance between his start and end points.
We are told that the man originally
runs 24 kilometers along a straight road. He then turns 139 degrees and runs
a further nine kilometers. We are asked to calculate the
shortest distance between his start and end points.
We know that angles on a straight
line sum to 180 degrees. And 180 minus 139 is equal to
41. This means that the angle inside
our triangle is 41 degrees. We can now calculate the shortest
distance labeled 𝑥 using the cosine rule. This states that 𝑎 squared is
equal to 𝑏 squared plus 𝑐 squared minus two 𝑏𝑐 multiplied by cos 𝐴. The side we’re trying to calculate
is opposite the given angle. Substituting in our values, we have
𝑥 squared is equal to 24 squared plus nine squared minus two multiplied by 24
multiplied by nine multiplied by cos of 41 degrees.
Typing the right-hand side into the
calculator gives us 330.9654 and so on. We then need to square root both
sides of this equation. This gives us 𝑥 is equal to
18.1924 and so on. We are asked to give our answer to
the nearest kilometer. Therefore, the one in the tenth
column is the deciding number. As this is less than five, we round
down. The shortest distance between the
start and end points to the nearest kilometer is 18 kilometers.
