The sun is 30 ∘ above the horizon. It makes a 54 m -long shadow of a tall tree.
the height of the tree is
... 54 tan(30º) m
31.17691454
or
31.2
To find the height of the tall tree, we can use the concept of similar triangles. Let's assume the height of the tree is represented by 'h'.
We know that the angle of elevation of the sun is 30 degrees. This means that the angle of depression from the top of the tree to the base of the shadow is also 30 degrees.
Using this information, we can form the following triangle:
/|
/ |
/ |
/ | h
/ |
/ |
/θ |
/______|
From this triangle, we can see that the opposite side is the length of the shadow, which is 54 meters.
Using the trigonometric ratio for tangent, we have:
tan(30°) = h / 54
We can solve for 'h' by multiplying both sides of the equation by 54:
54 * tan(30°) = h
Using a calculator, we can find the tangent of 30 degrees:
h ≈ 54 * 0.577 ≈ 31.158
Therefore, the height of the tall tree is approximately 31.158 meters.
To find the height of the tall tree, we can use a basic trigonometric concept called the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the angle is the elevation of the sun, and the opposite side is the height of the tree, while the adjacent side is the length of the tree's shadow.
Let's denote the height of the tree as h and the length of the shadow as s.
From the information given, we know that the angle of elevation of the sun is 30 degrees and the length of the shadow is 54 meters.
First, we need to find the tangent of the angle of elevation:
tan(30°) = h / s
Now we can substitute the values into the equation:
tan(30°) = h / 54
To find the value of h, we need to isolate it. We can do this by multiplying both sides of the equation by 54:
54 * tan(30°) = h
Using a calculator, we can find that tan(30°) is approximately 0.5774:
54 * 0.5774 = h
h ≈ 31.17
Therefore, the tree is approximately 31.17 meters tall.