All the triangles are similar, so the ratio of (long leg)/(short leg) is the same. The long leg of ΔADB is
.. AD = AC -DC = 20 -4
.. AD = 16
Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8
Selection D is appropriate.
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You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))
At Wolf-M-Up, Cost = 17.50 + 2.25(number of days)
At Fangs-R-Us, Cost = 24.25 + 1.5(number of days)
The costs are the same when [ 17.50 + 2.25 D = 24.25 + 1.5 D ].
Subtract 1.5D from each side: 17.50 + 0.75 D = 24.25
Subtract 17.50 from each side: 0.75 D = 6.75
Divide each side by 0.75 : <em>D = 9 days</em>
Substitute 9 for the number of days at either company,
and the cost is<em> $37.75</em> .
If you only want the wolf for a few days, then Wolf-M-Up is cheaper.
If you plan to keep it for more than 9 days, then Fangs-R-Us will cost less.
For exactly 9 days, both wolves will cost the same $37.75 .
There's many properties you can use to find an unknown angle.
There are too many to lists but one core example would be an isosceles triangle that has two adjacent sides and angles.
Let's say that the sides of an isosceles triangle are any number "x"
now since two sides of the triangle are the same we can add these two x's together.
x+x = 2x
now the other side of the triangle can be anything you like. We can call it 4x for this example.
now if we add them all together we'll get 4x+2x=6x
Now since the angles of a triangle add up to 180 degrees
we can equate 6x=180 leaving x to be 30.
Now since x belongs to both sides of the triangle we can say that both angles are congruent as well because the two sides of the triangle are congruent. This is a known triangle law.
Since both angles are now 30 degrees this will leave us with 2(30) = 60
now if we subtract 180 - 60 we'll get 120 which is the remainder of the 3rd angle of the side that corresponds with 4x.
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You can use this formula to solve this problem... it uses the surface area to find the volume.
V= (A^3/2)/(6√pi)
Substitute the surface area value into "A" and then solve as you would on paper. I'm sorry I couldn't show you the entire process but this should get you your answer. Plus if your teacher asks for work, I just set you up and everything else should be self explanatory.
But the answer is ----> 33.5 inches cubed
