Question

Please help!!!!!!!!!!!

Answer 1

Answer:

  (7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

  30°-60°-90° triangle: 1 : √3 : 2

  45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

  (7√3)/√2 = (7√6)/2

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Additional comment

Call the length of the horizontal line "y". Then the given ratios tell you ...

  7 : y = 1 : √3   ⇒   y/7 = √3/1   ⇒   y = 7√3

and

  x : y = 1 : √2   ⇒   x/y = 1/√2   ⇒   x = y/√2

When we rationalize the denominator, we get ...

  x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2