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MatroZZZ [7]
3 years ago
11

Find exact length of the third side

Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer:

37

Step-by-step explanation:

This is a right triangle so we can find the lengths by using the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

12^2 + 35^2 = c^2

144 +1225 = c^2

1369 = c^2

Take the square root of each side

sqrt(1369) = sqrt(c^2)

37 =c

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In the following picture, (QS) ̅ and (PR) ̅ are chords of the circle. Find the length of QS. (Remember to show formulas/equation
Inessa [10]
<h3>Answer: QS is 37 units long</h3>

=========================================

Explanation:

PN = 24 and NR = 14 are pieces of the chord PR. The two pieces multiply to some value. At the same time, the other two pieces QN = 21 and NS = 2x-4 also multiply to that same value. In short, the chord pieces multiply to the same number. This is known as the intersecting chord theorem.

PN*NR = QN*NS

24*14 = 21*(2x-4)

336 = 42x-84

336+84 = 42x-84+84 .... add 84 to both sides

420 = 42x

42x = 420

42x/42 = 420/42 ...... divide both sides by 42

x = 10

We know that x = 10 so we can use it to find the length of NS

NS = 2x-4

NS = 2*10-4

NS = 20-4

NS = 16

Therefore,

QS = QN + NS

QS = 21 + 16

QS = 37

--------

note: as a check,

PN*NR = QN*NS

24*14 = 21*16

336 = 336

we get a true equation, so we have the proper values

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3 years ago
What is the measure of x in the figure below?
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Answer:

115 degree

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