Given:
• Length of one side of the triangle = 400 ft
,
• Hypotenuse = x
,
• Length of smaller leg = y
,
• Complementary of one angle in the triangle = 31 degrees
Let's find the length of x.
Let's find the angle opposite the side with length 400 ft.
Since the complementary of the angle is 31 degrees, the measure of the angle is:
90 - 31 = 59 degrees.
Now, to find the length of x, apply trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
Where:
θ = 59 degrees
opposite side is the side opposite the angle = 400 ft
hypotenuse is the longest side of the right triangle = x
Plug in values and solve for x.
We have:
[tex]\begin{gathered} sin59=\frac{400}{x} \\ \\ x=\frac{400}{sin59} \\ \\ x=\frac{400}{0.8572} \\ \\ x=466.7\text{ ft} \end{gathered}[/tex]
Therefore, the value of x is 466.7 ft.
ANSWER:
466.7 ft
