Find height of tree from shadow silhouette

In summary, for the physics problems, the first one involves finding the height of a Christmas tree given the angle and base measurements of an isosceles triangle. The second problem involves finding the distance to the horizon from a person standing at the edge of the water, using the height of the person's eyes and the radius of the Earth. The third problem requires using the law of Cosines to find the angle facing the side of a triangle with given side lengths. Hints are provided to help solve the problems.
  • #1
hyen84
16
0
need help on physics problems

1)The silhouette of a Christmas tree is an isosceles triangle. The angle at the top of the triangle is 10.2 degrees, and the base measures 1.67 m across. How tall is the tree?

2) A person is standing at the edge of the water and looking out at the ocean (see figure). The height of the person's eyes above the water is h = 1.7 m, and the radius of the Earth is R = 6.37 x 106 m. (a) How far is it to the horizon? In other words, what is the distance d from the person's eyes to the horizon? (Note: At the horizon the angle between the line of sight and the radius of the Earth is 90 degrees.) (b) Express this distance in miles.

3.)Consider a triangle with sides 28.3, 143, and 128 cm in length. What is the angle facing the side of length 28.3 cm?

help me pleaseeeeeeeeeee...thanks in advanced
 
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  • #2
Have you tried them? Show some work.

Hints:

1. There is 180 degrees in a triangle. You know it's an isosceles triange so the other two angles are equal. Find all the angles of the triangle and apply the law of Sines.

2. I'd need to see the diagram to understand it completely.

3. Use the law of Cosines.
 
  • #3


1) To find the height of the Christmas tree, we can use the trigonometric tangent function. We know that the angle at the top of the triangle is 10.2 degrees and the base measures 1.67 m. Using the formula tan(angle) = opposite/adjacent, we can set up the equation as tan(10.2) = h/1.67. Solving for h, we get h = 0.296 m. Therefore, the height of the tree is 0.296 m.

2) To find the distance to the horizon, we can use the Pythagorean theorem. We know that the person's eyes are h = 1.7 m above the water, and the radius of the Earth is R = 6.37 x 106 m. The distance to the horizon, d, is the hypotenuse of a right triangle with sides h and R. Using the formula c = √(a^2 + b^2), we get d = √(1.7^2 + 6.37 x 10^6)^2 = 6.37 x 10^6 m. To express this distance in miles, we can convert it by multiplying by 0.6214. Therefore, the distance to the horizon is approximately 3,959 miles.

3) To find the angle facing the side of length 28.3 cm, we can use the Law of Cosines. The formula is c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite the angle C. Plugging in the values, we get 28.3^2 = 143^2 + 128^2 - 2(143)(128)cos(C). Solving for cos(C), we get cos(C) = 0.8906. Taking the inverse cosine, we get C = 27.9 degrees. Therefore, the angle facing the side of length 28.3 cm is approximately 27.9 degrees.
 

1. How do you measure the height of a tree from its shadow silhouette?

The height of a tree can be measured by using basic trigonometry. First, measure the length of the tree's shadow and the distance from the base of the tree to the end of the shadow. Then, use the formula height = (length of shadow * distance to tree) / length of tree.

2. Is it accurate to use the shadow silhouette to determine the height of a tree?

Using the shadow silhouette to determine the height of a tree can give an estimate, but it may not be completely accurate. Factors such as the angle of the sun, uneven terrain, or branches obstructing the shadow can affect the accuracy of the measurement.

3. Can the height of any tree be measured using this method?

Yes, this method can be used to measure the height of any tree, as long as the tree has a clearly defined shadow and there is a flat surface to measure the distance from the base of the tree to the end of the shadow.

4. Are there any other methods to determine the height of a tree?

Yes, there are other methods such as using a clinometer, a laser rangefinder, or climbing the tree and measuring its height with a measuring tape. However, using the shadow silhouette method is a simple and convenient way to estimate the height of a tree.

5. Why is it important to know the height of a tree?

Knowing the height of a tree can provide valuable information for various purposes. It can help in determining the age and growth rate of a tree, assessing its health, and planning for proper care and maintenance. It can also be useful in forestry, construction, and landscaping projects.

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