Question

Triangle A B C is shown as the path of a ferry. Side A B is 3.5 miles long. The ferry turns 75 degrees to side B C. Side B C is 6 miles long. Side C A has an unknown length d.
A ferry transports passengers to three different ports. From port A, the ferry travels east 3.5 miles to port B. The ship then turns 75° south and travels for 6 miles to reach port C. What is the distance d from port C to port A? Approximate to the nearest tenth of a mile.

miles

Answer 1

The length of C from A is 3.5 miles if AB=3.5 miles and BC is 6 miles .

Given The length of triangle ABC AB=3.5 miles , BC=6miles and AC=d

We have to find the value of d

First of all we have to draw a perpendicular from point A on side BC .

It forms two triangles ABE and AEC if E is the point where perpendicular stands on BC.

In triangle BEA

AE=$\sqrt{3.5^{2} -3^{2} }$

=$\sqrt{12.25-9}$

=$\sqrt{3.25}$

=1.8

Now in triangle AEC

AC=$\sqrt{1.8^{2} +3^{2} }$

=$\sqrt{3.24+9}$

=$\sqrt{12.24}$

=$\sqrt{12.24}$

=3.49 MILES

By rounding off to the nearest tenth we will get 3.4 miles

Hence the value of d is 3.4 miles.

Learn more about pythagoras theorem at https://brainly.com/question/27966159

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