Geometry help please!

- anonymous

Geometry help please!

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- anonymous

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- anonymous

please help me

- AccessDenied

should we assume that 'x' is the length of the altitude to the hypotenuse? If so, we only need to take the geometric mean of the hypotenuse segments
x 9
- = -; for x
5 x

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- anonymous

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- anonymous

I don't get it. x would =1.3

- AccessDenied

in the triangle, we have a 45-45-90 triangle. do you know how the legs of that triangle compare to the hypotenuse?

- anonymous

what would be the answers?

- AccessDenied

im not here to give you the answer, just help you get there. :(

- anonymous

what you are saying doesnt make sense

- AccessDenied

|dw:1333486260813:dw|
If this is what we know in the triangle, the last angle is 45, right? So, since the two angles are congruent, the legs are also congruent (isosceles triangle th). Pythagorean theorem to find the hypotenuse would be:
a^2 + a^2 = h^2
2a^2 = h^2
sqrt(2a^2) = sqrt(h^2)
a*sqrt(2) = h
this is true for all 45-45-90 triangles with a side length "a" and hypotenuse "h"

- anonymous

5(5)+5(5)=h(h)

- AccessDenied

yes, 5*5 + 5*5 = h^2 (although h is y in the context of our problem)

- anonymous

ok next it would be 2(5)*5=h*h

- anonymous

it is 50

- AccessDenied

yeah, you could do that
50 = h*h , then you take the positive square root of both sides (h*h = h^2)

- anonymous

the answer is b?

- AccessDenied

Yes. :)

- anonymous

can you help me on #1?

- AccessDenied

the first problem you posted? well, when we have an altitude that divides the opposite hypotenuse, it divides them in a way that we can set up certain ratios between the triangles.
|dw:1333486731312:dw|
Basically, we set it up as
\[ \frac{5}{x} = \frac{x}{9} \]
In words, we take the left hypotenuse segment (5) over the altitude (x) and set it equal to the altitude (x) over the right hypotenuse segment (9).
that's not the only way to write it necessarily, but I'll go with this way. they all work. then solve for x

- anonymous

x=22.5?

- AccessDenied

how do you get that?

- anonymous

5x=9x x=1.8?

- AccessDenied

to solve it, we cross-multiply, so we take the denominator of one side to the numerator of the other side
|dw:1333487031640:dw|

- anonymous

2x=45

- anonymous

x*x=45

- anonymous

the answer is a?

- AccessDenied

Yes. :)

- anonymous

I have 2 more problems to ask

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- anonymous

thank you so much

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- AccessDenied

for the first of the two, we can just look at b and 120 as supplementary
b + 120 = 180
the second one is exterior angle theorem, where the sum of nonadjacent interior angles are congruent to the opposite exterior angle

- anonymous

1=60?

- anonymous

2) 65+x=3x-5?

- anonymous

2)35?

- AccessDenied

Yes, #1 is 60
and #2 sounds correct as well

- anonymous

how do I do 3?

- AccessDenied

oh, there are two questions on the second thing! sec i gotta reorganize now. :P

- AccessDenied

for the first image, the b = 60 is correct
for the second image's first question, we'd have to find x and substitute it back into 3x - 5 to find the angle measure of the exterior angle (which conveniently answers the last question). Then since the exterior angle and b are supplementary, we add the b to the value and set it equal to 180 / solve for b.

- AccessDenied

the value of x was correctly 35, so we evaluate 3(35) - 5 for the exterior angle measure

- anonymous

how do I set up it up? I am kind of confused

- anonymous

answer = 100

- AccessDenied

yeah, that answers the very last question
then, we do the same thing as your first question with b and 120
they're supplementary, so we add them together and set = 180 to solve for b

- anonymous

do you me couple more. Please

- AccessDenied

b + 100 = 180
b = 80

- anonymous

do you mind helping me with a couple more?

- AccessDenied

i dont mind. :)

- anonymous

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- anonymous

5 problems total

- anonymous

thanks

- AccessDenied

For the first one, we're just looking at what we know.
we know two angles that are congruent, and we also have this bit:
|dw:1333488368342:dw|
But, since that segment between the two congruent segments is shared by both triangles, it is also congruent to itself, so we can see that those sides are congruent.

- AccessDenied

#2 we just use corresponding angles postulate / other angle theorems to trace the relation between the known angle 30* to angle 5
i.e. m<1 = 30 because of vertical angles
can we show the relation between m<1 and m<5?

- AccessDenied

for #3, we can use any of the three trig functions (sine, cosine, tangent) to find it since we know all three sides
just have to keep it straight that
sin t = opp/hyp, cos t = adj/hyp, and tan t = opp/adj
evaluate, round

- AccessDenied

well, not evaluate necessarily, solve for the angle by using inverse functions

- AccessDenied

#4: BD is the perpendicular bisector of the base, so its an isosceles triangle. we can use that information to find an equation with x.
#5: just take top of first triangle over top of second triangle
intuitively, we can see that by going from 10 to 5, we're halving the number, so the scale factor would be 1/2
10(1/2) = 5

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