2 2/3 as a improper fraction
2 answers:
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By applying the Pythagorean Theorem and the Trigonometry ratio, CAH, the value of cos(M) = 4/5
<em><u>Recall:</u></em>
Trigonometry ratios, <em>SOH CAH TOA</em> can be applied to solve a right triangle.
- Pythagorean Theorem can also be applied which is: c² = b² + a², where c is the longest side (hypotenuse length).
<em><u>Given:</u></em>
ΔMNL is a right triangle
ML = 25
NL = 15
Find MN using the Pythagorean Theorem:
MN = √(ML² - NL²)
MN = √(25² - 15²)
MN = 20
To find the value of cos(M), apply the trigonometry ratio, CAH, which is:
cos ∅ = Adj/Hyp
- Where,
∅ = M (reference angle)
Hypotenuse = ML = 25
Adjacent = MN = 20
- Plug in the values:
cos(M) = 20/25
cos(M) = 4/5
Learn more about Trigonometry ratios on:
Answer:
Length of the fence required = 135 m
Step-by-step explanation:
Total length of the fence required to cover the vacant lot = Perimeter of the isosceles trapezoid
Perimeter of ABCD = AB + BC + CD + AD
Since, AB = BC = EF = ED = 25 m
From the given right triangle BEC,
m∠EBC = m∠ECB = 45°
ΔBEC will be an isosceles triangle.
So, BE = EC
By Pythagoras theorem,
BC² = BE² + EC²
25² = 2(EC)²
EC = m
And DC = (DF + EF + EC)
= EC + EF + EC [Since, DF = EC]
= 2EC + EF
= 35.4 + 25
= 60.4 m
Hence. perimeter of ABCD = 25 + 25 + 60.4 + 25
= 135.4 m
≈ 135 m
Therefore, length of the fence required = 132 m
