Question

:)

Answer 1

Hey I've got to go. Go ahead bump it up and let some else give a go. If you still don't get an answer all look it later and get an answer to you.

Answer 2

I'm back

The first problem you solve by using proportions. I would suggest you take a piece of paper and fold it half. Then draw a large right triangle on the side opposite of the crease. Then cut the triangle out with a pair of scissors. This will give you two right triangles. Label one triangle ABC like your diagram, along with the side measurements x, 6 and y.

Cut the other triangle along the altitude, the segment AD. This will give you two more right triangles, a small one and a medium one. Label both of the triangles. The smaller one you will have to label on both sides, since you are going to flip it.

Answer 3

We will solve for x first. So grab the smaller and largest triangles and line them up right angle to right angle, hypotenuse to hypotenuse.

The hypotenuse of the large triangle is x. The hypotenuse of the smaller triangle is 6. The leg of the larger triangle is 6 and leg of the smaller triangle is x-9.

So your proportion will look like this.\[\frac{ x }{ 6 }=\frac{ 6 }{ x-9}\]

Answer 4

Cross multiple.

\[6*6=36\]\[x(x-9)=x ^{2}-9x\]
Set them equal to each other.\[x ^{2}-9x=36\]Rearrange\[x ^{2}-9x-36=0\]Solve for x using the quadratic equation or just plain factoring.

The we have this:
\[(x-12)(x+3)\] So the value of x is either -3 or 12 We discard -3 since the length can't be negative.

So x =12

Answer 5

To solve for y, grab the largest triangle and the medium triangle. Again line them up hypotenuse to hypotenuse and right angle to right angle

The hypotenuse is 12 for the large triangle and y for the medium triangle. The leg is y for the large triangle and 9 for the small triangle.

So the proportion will look like this:\[\frac{ 12 }{ y }=\frac{ y }{ 9 }\]

Answer 6

Cross multiply.
\[12*9=108\]
\[y*y=y ^{2}\]

Set them equal to each other.\[y ^{2}=108\]\[y=\sqrt{108}\]Simplify\[y=6\sqrt{3}\]

Answer 7

The second problem you will have to use right angle trigonometry.

We notice that the inside triangle is a 45,90,45 triangle so the legs of this triangle are the same length. So h=14ft.

To find angle y, we use the tangent trigonometric function. \[\tan = \frac{ side opposite the \angle }{ adjacent the \angle }\]\[\tan y=\frac{ 14 }{ 26}\]\[y=\tan^{-1} \frac{ 14 }{ 26 }\]
\[y \approx28.3 degrees\]

Answer 8

I gave you y. It's 28.3 degrees.

You can calculated the x angle a couple of ways.

One would be to note the the 45 degree angle at the bottom forms a straight line with an adjacent angle. So the adjacent angle would be 180-45 = 135 degrees.

Now you can find x by subtracting the y angle and the 135 degree angle from 180 degrees, since the sum of the angle in a triangle equal 180 degrees.

So you would have 180-135-28.3 = 16.7 degrees

So the x angle is 16.7 degrees.

Answer 9

Your welcome