A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of tree is 66 degrees. Determine the height of the tree, to the nearest foot.
Draw right triangle and high marked wid h, lenght of shadow marked wit s.
Angle off 66° betwen horizontal line and sloping line mark with á.
Then:
tan(á)=h/s
h=s*tan(á)
h=20*tan(66°)=20*2.246037=44.92074ft
In My answer á mean Greek letter Alpha
If the height of the building is 250 feet,the angle of the shadow is 49 degress, what is the distance from the top of a building to the tip of its shadow?
To determine the height of the tree, we can use trigonometry. In this case, we can use tangent (tan) since we have the length of the opposite side (height of the tree) and the length of the adjacent side (length of the shadow).
Let's define the height of the tree as 'h' and the length of the shadow as 's'.
Using the given information, we have:
s = 20 feet (length of the shadow)
angle = 66 degrees (angle of elevation)
Since tangent is defined as the ratio of the opposite side to the adjacent side, we can set up the equation:
tan(angle) = opposite/adjacent
tan(66 degrees) = h/20
Next, we can solve for 'h' by multiplying both sides of the equation by 20:
20 * tan(66 degrees) = h
Now, let's calculate the value of 'h':
h = 20 * tan(66 degrees)
Using a calculator, we find:
h ≈ 42.08 feet
Therefore, the height of the tree is approximately 42 feet (to the nearest foot).