The approximate value of ∠E is 109.5°
Step-by-step explanation:
Given is the triangle DEF
With sides
EF = d = 10
DF = e = 18
DE = f = 12
When we only know three sides of triangle, it is called SSS triangle. Law of cosines are used to solve these types of triangles.
Law of cosine to fine angle E will be:
[tex]cos\ E = \frac{d^2+f^2-e^2}{2df}[/tex]
Putting the values of d,e and f
[tex]cos\ E = \frac{(10)^2+(12)^2-(18)^2}{2(10)(12)}\\cos\ E = \frac{100+144-324}{240}\\cos\ E = \frac{-80}{240}\\cos\ E = \frac{-1}{3}\\E = cos^{-1} (\frac{-1}{3})\\E = 109.47[/tex]
Rounding off to nearest tenth
∠E = 109.5°
Hence,
The approximate value of ∠E is 109.5°
Keywords: Triangles, angles
Learn more about angles at:
- brainly.com/question/10382722
- brainly.com/question/10387593
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