Find height of tree from shadow silhouette

[hyen84]

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

 

[MikeH]

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.

 

[M98Ranger]

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.