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4 votes
Find the value of y.

A.

√(55)
B. 6
C.

8 √(3)
D.16​

Find the value of y. A. √(55) B. 6 C. 8 √(3) D.16​-example-1

1 Answer

4 votes

Answer:


y=√(55)

which agrees with answer A

Explanation:

Notice there are three right angle triangles for which we can apply the Pythagorean theorem:

In the small triangle at the bottom we have the Pythagorean theorem rendering:

(a)


5^2+y^2=x^2\\x^2=25+y^2

in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:

(b)


11^2+y^2=z^2\\z^2=121+y^2

and finally in the large right angle triangle:

(c)


z^2+x^2=16^2\\z^2=256-x^2

We can combine equations b and c to obtain:


121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2

and then combine this and (a) to get:


25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=√(55)

User Ron Savage
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