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In the figure below, find the exact value of z. (Do not approximate your answer.)

In the figure below, find the exact value of z. (Do not approximate your answer.)-example-1
User Lorlin
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1 Answer

2 votes

Answer:


z = (25)/(3)

Explanation:

Pythagora's Theorem

In any right triangle, the square of the measure of the hypotenuse is the sum of the squares of the legs. This can be expressed with the formula:


c^2=a^2+b^2

Where

c = Hypotenuse or largest side

a,b = Legs or shorter sides

We are required to find z in the figure provided. We have completed the construction with two additional variables h and x in the image below.

The triangle to the left side has hypotenuse 5 and one leg of 3, thus:


h^2=5^2-3^3=25-9=16


h=√(16)=4

Now for the bigger triangle:


z^2=5^2+x^2

Solving for
x^2


x^2=z^2-5^2

For the smaller right-side triangle:


x^2=4^2+(z-3)^2

Equating both equations:


z^2-5^2=4^2+(z-3)^2

Expanding the square:


z^2-5^2=4^2+z^2-6z+9

Simplifying and operating:


-25=16-6z+9


6z=25+25=50


z = (50)/(6)=(25)/(3)


\boxed{z = (25)/(3)}

In the figure below, find the exact value of z. (Do not approximate your answer.)-example-1
User Ser
by
6.7k points