The angle of elevation of the sun at 10:00 a.m. is 29 degree. At this point, a tree shadow's is 32 feet long. How tall is the tree?
IS THE ANSWER 15.5 FT?
tan29 = height/32
height = 32tan29 =17.7 ft
16 ft
To find the height of the tree, we can use the concept of trigonometry.
Let's consider a right-angled triangle where the vertical side is the height of the tree and the horizontal side is the length of the tree's shadow. The angle of elevation of the sun is the angle formed between the ground and the line from the top of the tree to the sun.
Now, to find the height of the tree, we can use the tangent function. The tangent of an angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the tangent of the angle of elevation is equal to the height of the tree divided by the length of the shadow.
Using the tangent formula:
Tan(angle) = height / shadow length
Plugging in the values:
Tan(29 degrees) = height / 32 feet
To find the height, we can rearrange the equation:
Height = Tan(29 degrees) * 32 feet
Calculating the height of the tree:
Height = 0.5543 * 32 feet
Height ≈ 17.74 feet
Therefore, the height of the tree is approximately 17.74 feet, not 15.5 feet.
To determine the height of the tree, you can use trigonometry and the given information about the angle of elevation and the length of the shadow.
First, let's label the diagram:
- Let x be the height of the tree.
- Let θ be the angle of elevation of the sun.
- Let h be the length of the shadow.
From the information given, we have:
- θ = 29 degrees
- h = 32 feet
To find the height of the tree, we can use the tangent function, which is defined as the ratio of the length of the opposite side (the height of the tree) to the length of the adjacent side (the shadow of the tree).
In this case, tan(θ) = x / h.
Rearranging the equation to isolate x:
x = tan(θ) * h.
Substituting the given values:
x = tan(29°) * 32 feet.
Using a calculator:
x ≈ 0.55431 * 32 feet ≈ 17.74 feet.
So, the height of the tree is approximately 17.74 feet.
Therefore, your answer of 15.5 feet is incorrect. The correct answer is approximately 17.74 feet.