Answer:
A. 336.4 ft
Step-by-step explanation:
To determine how high above the ground the kite is, we can model the scenario as a right triangle. Its hypotenuse represents the string of the kite (350 ft), and the angle of elevation between the base and the hypotenuse is 74°.
The height of the string above the ground represents the side of the triangle opposite the angle of elevation, so we can use the sine trigonometric ratio to find its length.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]
In this case:
Substitute the values into the sine ratio and solve for O:
[tex]\sin 74^{\circ}=\dfrac{O}{350}\\\\\\O=350\sin 74^{\circ}\\\\\\O=336.441593578...\\\\\\O=336.4\; \sf ft\;(nearest\;tenth)[/tex]
Therefore, the height of the kite above the ground is:
[tex]\LARGE\boxed{\boxed{336.4\;\sf ft}}[/tex]
