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:
k = -8
Step-by-step explanation:
The location of P is ...
P = (2A+B)/3 = (2·2+5, 2·1-8)/3 = (3, -2)
Putting this point into the equation for the line, we have ...
2(3) -(-2) +k = 0
8 +k = 0
k = -8
Answer:

Step-by-step explanation:
move the 2l to the other side by subtracting 2l on both sides. you get P - 2l = 2w. now divide both sides by 2 to get the answer.
<span> <u>24 + 3x = 3x + 3(7 - 1)</u>
Eliminate the parentheses: 24 + 3x = 3x + 3(6)
24 + 3x = 3x + 18
Subtract 3x from each side: <em>24 = 18</em>
Look at that for a second. Can ANY value of 'x' make 24 equal to 18 ?
I don't think so.
There's NO number that makes the equation a true statement.
That's just another way to say: "The equation has NO solution."</span>
Answer:
1.5 as decimal, 1 1/2 as a fraction
Step-by-step explanation:
1. convert 2 5/6 & (-1 4/12) to a improper fraction.
17/6 and -16/12
2. multiply 17/6 by 2 to match -16/12's denominator
17/6 * 2 = 34/12
We now have
34/12 + -16/12
A positive number plus a negative number is the same thing as subtraction so we remove the negative sign and replace the plus with a minus sign.
We have:

Now solve. 34-16 = 18
our answer is 18/12