how tall is a tree if it costs a shadow 59 degrees 24 minutes 41 inches on the ground 40 meter?
You need to rephrase the question, in better English. Are you sure the "41 inches" is not "41 arc seconds"? Is that angle the sun elevation angle? What does "on the ground 40 meter" mean? Is that the length of the shadow?
yes it is the lenght of the shadow.that is the problem that my professor gave me.
Theta = 59 deg 24' 41" = 59.4114 deg
is the solar elevation angle. (That is the angle that the sun is above the horizon)
Shadow length = 40 m = L cot (theta)
L = (Shadow length)*tan theta
= 40 tan 59.4114 = 67.67 m
A tree growing on a hillside casts a 121-foot shadow straight down
the hill. Find the height of the tree (in feet) if the slope of the hill is 8�
and the angle of elevation of the sun from the horizontal is 50�.
To determine the height of a tree using the information provided (shadow length, angle of elevation, and distance from the tree), we can apply the concept of trigonometry.
Step 1: Convert the angle from degrees, minutes, and seconds to decimal form.
The given angle is 59 degrees 24 minutes 41 inches. To convert this to decimal form, divide the number of minutes by 60 and add it to the number of degrees. Then divide the result by 60 and add it to the previous result.
59 degrees + (24 minutes / 60) + (41 inches / (12 inches per foot * 5280 feet per mile))
59 + (24 / 60) + (41 / (12 * 5280)) = 59.411421002
Now, we have the angle of elevation as approximately 59.411421002 degrees.
Step 2: Set up the trigonometric equation.
In this case, we will use the tangent function because we have the length of the shadow (41 inches) and the distance from the tree (40 meters). The tangent of an angle is equal to the height divided by the distance.
tan(angle) = height / distance
Step 3: Solve for the height.
Plugging in the values into the equation:
tan(59.411421002) = height / 40
Using a scientific calculator, we can find the value of the tangent for this angle:
tan(59.411421002) ≈ 1.779031
Multiply both sides of the equation by 40 to isolate the height:
1.779031 * 40 = height
The height of the tree is approximately 71.161241 meters (rounded to six decimal places).
Therefore, the height of the tree is approximately 71.161241 meters.