a. How far is the spot on the beach from the parking lot?
b. How far will he have to walk from the parking lot to get to the refreshment stand?
Show work please.
Answers
The altitude of the right triangle is the geometric mean of the 2 parts of the side it separates.
a. The answer would be sqrt(18*32)=24
The question to the second question can be answered by using the Pythagorean theorem.
32^2+24^2=1600=40^2
b. The answer would be sqrt40^2=40
The beach, the parking lot and the refreshment stand are illustrations of similar triangles.
The distance between the spot and the parking lot is 24 mThe distance between the refreshment stand and the parking lot is 40 m(a) The distance between the spot and the parking lot
Represent this distance with d.
So, the equivalent ratio is:
[tex]\mathbf{32:d = d : 18}[/tex]
Express as fractions
[tex]\mathbf{\frac {32}d = \frac{d}{ 18}}[/tex]
Cross multiply
[tex]\mathbf{d \times d = 32 \times 18}[/tex]
[tex]\mathbf{d^2 = 576}[/tex]
Take square roots
[tex]\mathbf{d = 24}[/tex]
Hence, the distance between the spot and the parking lot is 24 m
(b) The distance between the refreshment stand and the parking lot
Represent this distance with d.
Using Pythagoras theorem we have:
[tex]\mathbf{d^2 = 32^2 + 24^2}[/tex]
[tex]\mathbf{d^2 = 1600}[/tex]
Take square roots
[tex]\mathbf{d = 40}[/tex]
Hence, the distance between the refreshment stand and the parking lot is 40 m
Read more about similar triangles at:
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