What is the difference between defined and undefined terms?
2 answers:
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Given:
Height of the lighthouse = 280 feet
The angle of depression from the top of the lighthouse to a ship = 18°.
To find:
The distance between boat and shore.
Solution:
Draw a diagram by using the given information.
In a right angle triangle,
In triangle ABC,
Using a calculator, we get
Therefore, the boat is 862 feet away from shore.
A) Pine Road and Oak Street form a right angle, so we can extract the relation
where
is the distance we want to find (bottom side of the rectangle).
Alternatively, we can use the other given angle by solving for in
but we'll find the same solution either way.
b) Pine Road and Oak Street form a right triangle, with Main Street as its hypotenuse. We can use the Pythagorean theorem to find how long it is.
Let
be the length of Main Street. Then
but of course the distance has to be positive, so
.
where
Alternatively, we can use the other given angle by solving for
but we'll find the same solution either way.
b) Pine Road and Oak Street form a right triangle, with Main Street as its hypotenuse. We can use the Pythagorean theorem to find how long it is.
Let
but of course the distance has to be positive, so