Given:
A figure of a right triangle with perpendicular 500 m and hypotenuse x.
To find:
The value of x.
Solution:
If a transversal line intersect two parallel lines, then alternate interior angles are congruent.
Using the above definition the measure of angle opposite to the perpendicular is 40 degrees.
In a right angle triangle,
[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin 40^\circ =\dfrac{500}{x}[/tex]
[tex]x=\dfrac{500}{\sin 40^\circ }[/tex]
[tex]x=\dfrac{500}{0.6427876}[/tex]
[tex]x=777.8619[/tex]
Round the value to the nearest tenth.
[tex]x\approx 777.9[/tex]
Therefore, the value of x is 777.9 m.