Answer: x = 108
Step-by-step explanation: In this problem, we're given a diagram and
we're asked to find the value of x that would make m ll n.
We can see that the angles that are marked in the diagram
are same-side interior angles since they lie on the same side
of the transversal and they lie on the interior of lines m and n.
Therefore, in order for line m to be parallel to line n,
these angles must be supplementary.
In other words, they must add to 180 degrees.
So we can setup the equation x + 72 = 180.
Subtracting 72 from both sides gives us x = 108.
So the value of x that would make line m ll n is 108.
Pythagoras theorem: leg 1 squared + leg 2 squared = hypotenuse squared
In the diagram, the triangle has angles 90 and 45. So the other angle in the triangle must be 45 degrees as well. (180 - 90 -45 = 45)
This means it is an isosceles triangle (since two angles are the same), so the two legs have the same length.
So we can say that length of leg1 = x, and the length of leg2 also equals x
Now let's use pythagoras' theorem:
leg1 = x
leg2 = x
hypotenuse = 16
x^2 + x^2 = 16^2
2x^2 = 16^2
2x^2 = 256
x^2 = 128
x = √(128)
x = 8√2
Answer:
11.820 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...
sin(52°) = height/(15 ft)
Multiplying by the denominator gives you ...
height = (15 ft)·sin(52°) ≈ 11.820 ft
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You may need to round this number appropriately.
Here
360 = 24%
360=24/100
360*100=24
36000/24=1500 so ur answer is 1500
