Respuesta :

Answer:

The length of the hypotenuse is of 143 ft.

Step-by-step explanation:

Relations in a right triangle:

The cosine of an angle [tex]\theta[/tex], in a right triangle, is given by the length of the adjacent side divided by the length of the hypotenuse.

In this question:

[tex]\cos{43} = \frac{109}{h}[/tex]

Using a calculator, the cosine of 43 degrees is of 0.73135. So

[tex]0.73135 = \frac{109}{h}[/tex]

[tex]0.73135h = 109[/tex]

[tex]h = \frac{109}{0.73135}[/tex]

[tex]h = 149[/tex]

The length of the hypotenuse is of 143 ft.