1. Using the figure below, what is the measure of angle ABE?
2 answers:
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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.
Answer:
Step-by-step explanation:
<u>Rational Numbers</u>
A rational number is any number that can be expressed as a fraction
for a and b any integer and b different from 0.
As a consequence, any number that cannot be expressed as a fraction or rational number is defined as an Irrational number.
Let's analyze each one of the given options
The first part of the number is indeed a rational number, but the second part is a square root whose result cannot be expressed as a rational, thus the number is not rational
The second part is an exact square root (resulting 4) but the first part is a known irrational number called pi. It's not possible to express pi as a fraction, thus the number is irrational
The square root of 121 is 11. It makes the whole number a sum of a rational number plus an integer, thus the given number is rational
As with the first number, the square root is not exact. The sum of a rational number plus an irrational number gives an irrational number.
Correct option: