Find the exact value of the​ following, without using a calculator.

9514 1404 393

  (√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

  sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

  cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

  sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

  cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

  sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

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step-by-step explanation:

123123 step byt step

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584