Answer:
119.2 m
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the height of the triangle represents the diameter of the Ferris wheel (100 m), and the hypotenuse represents the distance between Iris and the topmost point of the Ferris wheel.
Given that the angle of depression from the topmost point of the Ferris wheel to Iris is 57°, then, according to the Alternative Interior Angles Theorem, the angle between the base and the hypotenuse of the right triangle is also 57°.
To find the distance (d) that Enrique and Trina are from Iris when they are at the topmost point of the Ferris Wheel, we can use the sine trigonometric ratio:
[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 distance (d):
[tex]\sin 57^{\circ}=\dfrac{100}{d}\\\\\\d=\dfrac{100}{\sin 57^{\circ}}\\\\\\d=119.23632928...\\\\\\d=119.2\; \sf m\;(nearest\;tenth)[/tex]
Therefore, Enrique and Trina are 119.2 m away from Iris.
