9514 1404 393
Answer:
437.3 ft
Step-by-step explanation:
The angle of depression can be copied inside the triangle to the angle of elevation (at lower right). Then the side x can be seen to be adjacent to the angle.
The mnemonic SOH CAH TOA reminds you of the relations. Here, we have the hypotenuse and we want the adjacent angle. The relevant relation is ...
Cos = Adjacent/Hypotenuse
cos(29°) = x/(500 ft)
Multiplying by 500 ft gives ...
x = (500 ft)cos(29°)
x ≈ 437.3 ft
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Additional comment
You have posted a number of problems that make use of this geometry. They are all solved the same way:
a) identify the desired measure and the given measures
b) using SOH CAH TOA, identify the relation applicable to those measures
c) fill in the given values in the equation
d) solve for the unknown
You may need to make use of what you know about angles and triangles in order to relate given angles to ones you need to use.
