For the given triangle, x measures 437.3 feet.
Step-by-step explanation:
Step 1:
The total angle of a right-angle is 90°. There is a right angle at the top of the triangle.
The sum of the top angle of the triangle and the given 29° is 90°.
So the angle of the triangle [tex]= 90 - 29 = 61.[/tex]
So the angle of the triangle at the top end is 61°.
Step 2:
For the top angle, x is its opposite side while the hypotenuse is represented by the side measuring 500 feet.
To determine the value of x, we determine the sine of the angle.
[tex]sin \theta= \frac{oppositeside}{hypotenuse} .[/tex]
[tex]sin 61 = \frac{x}{500} , sin 61 = 0.874.[/tex]
[tex]x = (0.8746)(500) = 437.3[/tex]
So rounding this off, we get x measures 437.3 feet.
