Solve for X. Show work please. Thank you so much :) The photo of the problem is provided. No worries :)
1 answer:
Answer:
x = 9.36
Step-by-step explanation:
Add a few more lines.
We can show that the three triangles are similar as they each have a right angle and share the common angle to the right.
D = 2R = 33.4
Purple triangle
y² = (33.4 - x))² + 15²
y² = 1,115.56 - 66.8x + x² + 225
y² = x² - 66.8x + 1,340.56
red triangle
x² + 15² = z²
Green triangle
y² = 33.4² - z²
y² = 33.4² - x² - 15²
y² = 890.56 - x²
We now have two equations for y²
x² - 66.8x + 1,340.56 = 890.56 - x²
2x² - 66.8x + 450 = 0
x² - 33.4x + 225 = 0
x = (33.4 ±√(33.4² - 4(1)(225))) / 2(1)
x = 24.0409... ignore as it is bigger than R
or
x = 9.359019...
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