Answer:
D. [tex]e=8.9\ cm[/tex]
Step-by-step explanation:
Given:
In triangle BTE
ET = 5 cm
BE = 6 cm
BT = [tex]e[/tex]
m∠E= 108°
To find the approximate value of [tex]e[/tex].
Solution:
We can apply cosine law to find the value of [tex]e[/tex]
By cosine law:
[tex]c=\sqrt{a^2+b^2-2ab\cos C}[/tex]
where [tex]a[/tex] and [tex]b[/tex] adjacent sides such that ∠C is the angle between them.
For the given triangle the cosine law would be represented as:
[tex]e=\sqrt{5^2+6^2-2(5)(6)\cos 108}[/tex]
Solving for [tex]e[/tex]
[tex]e=\sqrt{25+36-60(-0.30)}[/tex]
[tex]e=\sqrt{25+36+18}[/tex]
[tex]e=\sqrt{79}[/tex]
[tex]e=8.88\approx 8.9 cm[/tex]
