We are looking for the value of the second integer, so let's mark it as X.
Then three consecutive integers are : (x-1) , x , (x+1)
The sum of the first and the third integers (X-1) + (X+1)
Five less than three times the second integer 3X - 5
Now we can write an equation and solve it for X
(X-1)+(X+1)= 3X - 5 simplifying left part
2X = 3X -5 subtract 2X from both sides
0 = X-5
X=5
SO THREE CONSECUTIVE INTEGERS ARE 4, 5, 6
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Answer:
(15/17 = sin ∠ JLK)
(first option listed)
Explanation:
the "sin ∠ JLK" is what we can simply think of as the inside measurement of angle/corner L. (L is the letter in the middle of ∠ JLK , and if you imagine drawing a line from J to L to K, you would see that the only angle you formed both sides of is corner L)
so, we are looking for the sin of L.
(SOH CAH TOA)
we know that
sin = opposite / hypotenuse
However, we do not have the opposite value of this triangle <em>yet. </em>
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we can solve the length of the opposite side with the Pythagorean theorem:
a² + b² = c²
8² + b² = 17²
64 + b² = 289
- 64 - 64
b² = 225
√b² = √225
b = 15
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so, to solve for sin L,
(sin = opposite / hypotenuse)
we should divide the opposite (15) over the hypotenuse (17)
so, 15 / 17 = sin L
(15/17 = sin ∠ JLK)
