A pilot flying between two cities must fly out of her way to

A pilot flying between two cities must fly out of her way to avoid a storm. She flies 100 miles away from city A before turning 53degree toward city B. It is known that the two cities are 170 miles apart. After turning, how many more miles must she fly in order to reach city B? Round your answer to the nearest tenth of a mile. B A passenger on a jet measures the angle of depression to a landmark to be 24 degree. One minute later, the passenger measures the angle of depression to the landmark to be 56degree. Assuming the jet is flying at 620 mph, at a constant lavation, how high is it flying? Give your answer in feet, rounded to a whole umber 1 mile = 5280 feet. Watch your units! ?

Solution

1) So, we have a triangle with two sides given and an angle between a known side

and unknown side is given

We apply cosine rule :Lets assume she flies x miles to reach B

So, 100mi, x have an angle (180 -53) between them

So, c^2 = a^2 +b^2 - 2abcos(180 -53)

170^2 = 100^2 + x^2 - 2*100*xcos127

x^2 + 120.36x -18900 =0

Solve the quadratic: x= 89.89, -210.25 neglect the negative root

So, x = 89.89 = 89.9 miles