Choose the two equal expressions
2 answers:
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<h2>Hello!</h2>
The answer is:
The height of the lightning rod is 27.4 feet.
<h2>Why?</h2>To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.
So, writing the equations we have:
We know that the angle of elevation from the base of the buildings is 36°
Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.
Using the information we have:
To the top of the building:
To the top of the lightning rod:
Now, isolating we have:
Also, we have that:
Therefore, if we want to calculate the height of the lightning rod, we need to do the following:
Let "x" the distance to the top of the building and "y" the distance to the top of the lightning rod, so:
Rounding to the nearest foot, we have:
Hence, the answer is:
The height of the lightning rod is 27.4 feet.
Have a nice day!
The horizontal distance between Carl and the rock at sea is approximately 60.62ft.
Data;
- Angle = 30 degree
- Opposite = 35
- Adjacent = x
Given the angle of depression from his point to the sea, we can use trigonometric ratio to calculate for the horizontal distance from his location to the bottom of the sea.
SOHCAHTOA
Since we have the value of angle and opposite and we need to calculate the adjacent side of the right-angle triangle, we can use the tangent of the angle to this effect.
The horizontal distance between Carl and the rock at sea is approximately 60.62ft.
Learn more on trigonometric ratio here;