At a horizontal distance of 34 meters from the base of a tower, the angle of elevation to the top is 72 degrees. Find the line of sight distance to the nearest meter.
I set this up tan72=x/34
I believe your set up finds the height of the tower. The line of sight to the BASE of the tower is 34 meters by measurement. The line of sight to the TOP of the tower is cos 72 = 34/x
so the nearest meter would be 110.0
yes
thank you
To find the line of sight distance to the nearest meter, we can use the tangent function.
First, let's define the variables:
x - line of sight distance (the distance from the observer to the top of the tower)
34 - horizontal distance (the distance from the base of the tower to the observer)
72 degrees - angle of elevation to the top of the tower
Using the tangent function, we can set up the equation:
tan(72 degrees) = x/34
Now, let's solve for x:
Multiply both sides of the equation by 34:
34 * tan(72 degrees) = x
Using a calculator, calculate the value of tan(72 degrees), which is approximately 3.07768.
Therefore,
34 * 3.07768 ≈ 104.75112.
Now, rounding to the nearest meter, we get:
x ≈ 105 meters.
So, the line of sight distance to the nearest meter is 105 meters.