Find the values of x and y.

x = 4 , y = 8

Step-by-step explanation:

Using the sine ratio in the right triangle on the left and the exact value

sin45° =

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° = = = ( cross- multiply )

2h = 8 ( divide both sides by 2 )

h = 4

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Using the tangent ratio in the right triangle on the right and the exact value

tan30° = , then

tan30° = = = = ( cross- multiply )

x = 4

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Using the sine ratio in the right triangle on the right and the exact value

sin30° = , then

sin30° = = = ( cross- multiply )

y =8

The greatest possible integer in the set could be 43.

Explanation

Range is the difference between largest and smallest terms in the set. That means...

Now for getting the maximized largest number, we need to maximize the smallest number as the range 25 is fixed.

As the set has total 15 terms, so the median will be the 8th term. That means, there will be 7 terms before the median 25.

So, the maximized smallest number will be: 25 - 7 = 18 (As all the terms are different integers)

Thus, the possible greatest number