Answer:
8/17
Step-by-step explanation:
The correct and complete question is:
<em>Use △XYZ, in which ∠X is a right angle and tanY=8/15. What is the ratio for sinY?</em>
From definition:
tan(Y) = opposite/adjacent
From the graph and the question:
tan(Y) = XZ/XY = 8/15
Then:
XZ = 8 and XY = 15. Using pytaghorean theorem:
XZ² + XY² = YZ²
8² + 15² = YZ²
√289 = YZ
17 = YZ
From definition:
sin(Y) = opposite/hypotenuse
From the graph:
sin(Y) = XZ/YZ
sin(Y)= 8/17
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To solve this, set up two equations using the information you're given. Let's call our two numbers a and b:
1) D<span>ifference of two numbers is 90
a - b (difference of two numbers) = 90
2) The quotient of these two numbers is 10
a/b (quotient of the two numbers) = 10
Now you can solve for the two numbers.
1) Solve the second equation for one of the variables. Let's solve for a:
a/b = 10
a = 10b
2) Plug a =10b into the first equation and solve for the value of b:
a - b = 90
10b - b = 90
9b = 90
b = 10
3) Using b = 10, plug it back into one of the equations to find the value of a. I'll plug it back into the first equation:
a - b = 90
a - 10 = 90
a = 100
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Answer: The numbers are 100 and 10</span>
