We will solve this using a system of equations. The first part tells us that building a is 190 feet shorter than building b. Our first equation, then, is b=190+a. The second part tells us that the addition of the two buildings' heights is 1480. So our second equation is a + b = 1480. The first equation is already solved for b, so let's sub that value into the second equation for b: a+(190+a)=1480. 2a + 190 = 1480 and 2a = 1290. That means that building a is 645 feet tall. Building b is 190 feet taller, so b = 190 + 645, which is 835.
If <em>c</em> > 0, then <em>f(x</em> - <em>c)</em> is a shift of <em>f(x)</em> by <em>c</em> units to the right, and <em>f(x</em> + <em>c)</em> is a shift by <em>c</em> units to the left.
If <em>d</em> > 0, then <em>f(x)</em> - <em>d</em> is a shift by <em>d</em> units downward, and <em>f(x)</em> + <em>d</em> is a shift by <em>d</em> units upward.
Let <em>g(x)</em> = <em>x</em>. Then <em>f(x)</em> = <em>g(x</em> + <em>a)</em> - <em>b</em> = (<em>x</em> + <em>a</em>) - <em>b</em>. So to get <em>g(x)</em>, we translate <em>f(x)</em> to the left by <em>a</em> units, and down by <em>b</em> units.
Note that we can also interpret the translation as
• a shift upward of <em>a</em> - <em>b</em> units, since
(<em>x</em> + <em>a</em>) - <em>b</em> = <em>x</em> + (<em>a</em> - <em>b</em>)
• a shift <em>b</em> units to the right and <em>a</em> units upward, since
(<em>x</em> + <em>a</em>) - <em>b</em> = <em>x</em> + (<em>a</em> - <em>b</em>) = <em>x</em> + (- <em>b</em> + <em>a</em>) = (<em>x</em> - <em>b</em>) + <em>a</em>.
Well assuming that this would be a typical triangle, and not a right angle one, knowing that the sum of all sides adds up to 180 degrees, simply add all of the expressions and one value and make it equal to 180, and then solve for x.
(6x-1) + (X+14) + 20 = 180
6x - 1 + X + 14 = 160
7x - 1 + 14 = 160
7x + 13 = 160
7x = 147
X = 21.
Now solve for the angles by plugging in X.
A = 6x - 1 = 6(21) - 1 = 125 degrees
C = X + 14 = (21) + 14 = 35 degrees.
I believe these are the solutions.
Answer: 19.5
Step-by-step explanation:
Use Pythagorean theorem to find the diagonal as it is a right triangle.