The value of x in the diagram to the nearest tenth is x = 776.8 ft
How to find the hypotenuse side of a right-angle triangle.
The hypotenuse side of a right-angled triangle can be determined by using the Pythagoras rule if the opposite side and the adjacent side are known.
However, if an angle and the side are known, we can use the tangent of the trigonometry to determine the adjacent side, then use the Pythagoras rule to determine the hypotenuse.
tan 31 = 400/y
y = 400 / tan 31
y = 400 / 0.60086
y = 665.7
y ≅ 666
x² = 666² + 400²
[tex]\mathbf{x = \sqrt{666^2 + 400^2}}[/tex]
[tex]\mathbf{x = \sqrt{443556 + 160000}}[/tex]
[tex]\mathbf{x = \sqrt{603556}}[/tex]
x = 776.8 ft
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