Trigonometry

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

Trigonometry

Postby Guest » Sat Mar 02, 2019 9:02 pm

If side P = 8cm, Q = 7cm and side R = 5cm. So the area of the triangle is?
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Re: Trigonometry

Postby Guest » Tue Mar 05, 2019 2:19 am

a=8 ; b=7 ; c=5 ; [tex]S_{ABC }[/tex]=?

(cos T) [tex]a^{2}[/tex]=[tex]b^{2}[/tex]+[tex]c^{2}[/tex]-2bc.cos[tex]\alpha[/tex]

cos[tex]\alpha[/tex]=[tex]\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

cos[tex]\alpha[/tex]=[tex]\frac{49+25-64}{2.7.5}[/tex]

cos[tex]\alpha[/tex]=[tex]\frac{1}{7}[/tex] [tex]\Leftrightarrow[/tex] sin[tex]\alpha[/tex]=[tex]\sqrt{\frac{48}{49}}[/tex]

sin[tex]\alpha[/tex]=[tex]\frac{4\sqrt{3}}{7}[/tex] :!:

[tex]S_{ABC }[/tex]=[tex]\frac{bc.sin\alpha}{2}[/tex]=[tex]\frac{7.5.4\sqrt{3}}{2.7}[/tex]

[tex]S_{ABC }[/tex]=10[tex]\sqrt{3}[/tex] :D
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