Between which two consecutive integers does square root of 117 lie?
2 answers:
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Answer:
23.32 degrees
Step-by-step explanation:
We set up a large right triangle that has 2 triangles within it. The large triangle is a right triangle. The height of it is the height of the tower, the base angle is 62, the hypotenuse is 95, and the base measure is y. The other triangle has the same height which is the height of the tower, the angle is what we are looking for, and the base measure is 150 feet beyond y, so its measure is y + 150. We have enough information to find the height of the tower, so let's do that first. Going back to the first smaller triangle.
so the height of the tower is 83.88 feet. Now we need to solve for y. Using that same triangle and the tangent ratio, we find that
. Now let's do the same thing for the other triangle with the unknown angle.
Solve both of these for y. The first one solved for y:
The second one solved for y will simplify to:
Now that these are both solved for y, and y = y, we can set them equal to each other by the transitive property of equality:
Cross multiply to get this big long messy looking thing:
Distribute through the parenthesis to get
Get the unknown angles on the same side so it can be factored out:
And then factoring it out gives you:
Divide to get
Do this on your calculator in degree mode to give you an angle measure of 23.32°. I know this is really hard to follow without being able to draw the pics for you like I do in my classroom, but hopefully you can follow my description and draw your own triangles and follow from that!
Answer:
see the attachment
Step-by-step explanation:
If the growth is 7 feet in 2 weeks and the rate is constant, then it will be half that in one week, or 3.5 feet per week. At week 3, it will be 3.5 feet more than at week 2. The table below shows this progression.
The point (0, 0) means there was no measurable growth when time was starting to be measured (at week 0).
