Answer:
233 ft.
Step-by-step explanation:
Recall that an angle of depression is the angle in a right triangle that points downward.
Knowing that a right's triangle's angle is a piece of given information in this problem, we know that our problem is just right triangles trigonometry!
We can first start off by drawing a right triangle.
They tell us the height of the helicopter relative to the coast, 1450 feet, this represents the vertical leg of our right triangle.
They also tell us that the angle of depression from the helicopter is 41 degrees, this is the angle measure of the top right angle in our triangle and that the top right point should be labelling H or helicopter.
Finally, the problem asks how far the helicopter is from the coast, since the coast is always on the ground, we can label the bottom left point in the triangle as C or coast and, label the horizontal leg as d to represent the horizontal distance between C and H.
Recall SOH-CAH-TOA or [tex]\rm Sin(x)= \:\frac{Opposite}{Hypotenuse} \:\: Cos(x)=\frac{Adjacent}{Hypotenuse} \:\:Tan(x)=\frac{Opposite}{Adjacent}[/tex], where x is the reference angle that determines whether a leg is the opposite or adjacent side.
We're given an angle, a side length that's adjacent to that angle and we need to find the side length opposite to that angle. This follows tangent or Tan(x) out of the three basic trigonometric ratios!
Plugging what we know into the ratio,
[tex]\rm tan(41)=\frac{d}{1450}[/tex].
All there's left to finding d is the rearrange the equation and compute!
[tex]\rm 1450tan(41)=d=232.952=233ft[/tex]
