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Question Number 216855 by BaliramKumar last updated on 23/Feb/25

Answered by AntonCWX08 last updated on 23/Feb/25

Commented by AntonCWX08 last updated on 23/Feb/25

$$s=\frac{51+36+75}{2}=81$$$$Areaoftriangle=\sqrt{81(81-36)(81-51)(81-75)}=810$$$$\frac{1}{2}\left(36\right)\left(h\right)=810\Rightarrow h=45$$$$a=\frac{36\times 45}{36+45}=20$$

Commented by AntonCWX08 last updated on 23/Feb/25

$$Sorry,thexandangle{didn}^{\prime }tcontributetoanythinghere.$$

Commented by Ari last updated on 25/Feb/25

$$whya=\frac{36\times 45}{36+45}????????$$

Answered by mehdee7396 last updated on 26/Feb/25

$$cosB=\frac{{51}^2+{36}^2-{75}^2}{2\left(51\right)\left(36\right)}=0.47\Rightarrow sinB=0.78$$$$cotB=\frac{47}{78}$$$$cosC=\frac{{75}^2+{36}^2-{51}^2}{2\left(75\right)\left(36\right)}=0.8\Rightarrow sinC=0.6$$$$cotC=\frac{5}{3}$$$$acotB+a+acotC=36$$$$\frac{47}{78}a+a+\frac{5}{3}a=36\Rightarrow 47a+78a+150a=2808$$$$275a=2808$$$$a=\frac{2808}{275}=10.2$$$$$$

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