FIND THE HEIGHT OF A TREE,IF 120 FT. FROM ITS BASE THE ANGLE OF ELEVATION OF ITS TOP IS 10 DEGREE 18 MINUTES
well, we have
h/120 = tan 10°18'
h = 21.8 ft
we have 120 ft and 10 degree 18 minutes.
tan10*18'= height/120ft
height= 22ft
To find the height of the tree, we can use trigonometry and the given information about the angle of elevation.
In this scenario, we have a right triangle formed by the tree, the distance from the base to the observer, and the angle of elevation. The height of the tree is the opposite side (h), the distance from the base to the observer is the adjacent side (120 ft), and the angle of elevation is the angle between the horizontal line and the line of sight to the top of the tree.
To solve this problem, we need to use the tangent function:
tan(angle) = opposite/adjacent
In this case, angle = 10 degrees 18 minutes. To convert this angle to decimal degrees, we add the minutes fraction (18/60) to the degrees:
angle = 10 + 18/60 = 10.3 degrees
Now we can use the tangent formula:
tan(10.3 degrees) = h/120
We can solve for h by multiplying both sides of the equation by 120:
h = 120 * tan(10.3 degrees)
Using a calculator, we can find the value of tan(10.3 degrees):
tan(10.3 degrees) ≈ 0.1821
Now we can substitute this value back into the equation:
h ≈ 120 * 0.1821
h ≈ 21.85 ft
Therefore, the height of the tree is approximately 21.85 feet.