X = 4.33333333333
y = 5.33333333333
z = 6.33333333333
Answer:
You can use either of the following to find "a":
- Pythagorean theorem
- Law of Cosines
Step-by-step explanation:
It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.
I find it reasonably convenient to find the length of x using the sine of the 70° angle:
x = (15 ft)/sin(70°)
x ≈ 15.96 ft
That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.
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Consider the diagram below. The relation between DE and AE can be written as ...
DE/AE = tan(70°)
AE = DE/tan(70°) = DE·tan(20°)
AE = 15·tan(20°) ≈ 5.459554
Then the length EC is ...
EC = AC - AE
EC = 6.3 - DE·tan(20°) ≈ 0.840446
Now, we can find DC using the Pythagorean theorem:
DC² = DE² + EC²
DC = √(15² +0.840446²) ≈ 15.023527
a ≈ 15.02 ft
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You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)
DC² = AD² + AC² - 2·AD·AC·cos(A)
a² = x² +6.3² -2·6.3x·cos(70°) ≈ 225.70635
a = √225.70635 ≈ 15.0235 . . . feet
Your answer will be letter b
It takes a while to see through this one.
I think that's because the triangle is in a weird position.
The arrows on the two across-lines tell us that those lines are parallel.
And THAT tells us that the two triangles are similar ... the whole big triangle,
and the smaller triangle on the bottom.
If two triangles are similar, then what ?
-- Their corresponding angles are equal. That doesn't help us in this problem.
-- Their corresponding sides are in the same ratio. That helps us a lot !
The left side of the big triangle = 5 + 8 = 13
The left side of the small triangle = 8
Now we know that corresponding sides of the two triangles
have the ratio of 13 to 8 .
The right side of the big triangle = 4 + x
The right side of the small triangle = x
The ratio has to be 13/8 , so ===> (4+x) / x = 13 / 8 .
That's the tough part. Now you take it and finish it off from here.