The two triangles are similar, What is the length of DE?
1 answer:
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Answer:
174.6 ft
Step-by-step explanation:
It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)
We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...
180° -30° -112° = 38°
Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.
c/sin(C) = a/sin(A)
c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft
The height of the tree is about 174.6 feet.
The solutions for the quadratic equation are given as follows:
x = -1, x = 7/5
<h3>What is a quadratic function?</h3>A quadratic function is given according to the following rule:
y = ax^2 + bx + c
The solutions are:
In which:
For this problem, the equation is:
5x² - 2x - 7 = 0.
Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:
The solutions are:
x = -1, x = 7/5
More can be learned about quadratic equations at brainly.com/question/24737967
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