Question-216855

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

A r e a o f t r i a n g l e = \sqrt{81 (81 - 36) (81 - 51) (81 - 75)} = 810

\frac{1}{2} (36) (h) = 810 \Rightarrow h = 45

a = \frac{36 \times 45}{36 + 45} = 20

Commented by AntonCWX08 last updated on 23/Feb/25

S o r r y, t h e x a n d a n g l e {d i d n}^{'} t c o n t r i b u t e t o a n y t h i n g h e r e .

Commented by Ari last updated on 25/Feb/25

w h y a = \frac{36 \times 45}{36 + 45} ? ? ? ? ? ? ? ?

Answered by mehdee7396 last updated on 26/Feb/25

c o s B = \frac{51^{2} + 36^{2} - 75^{2}}{2 (51) (36)} = 0.47 \Rightarrow s i n B = 0.78

c o t B = \frac{47}{78}

c o s C = \frac{75^{2} + 36^{2} - 51^{2}}{2 (75) (36)} = 0.8 \Rightarrow s i n C = 0.6

c o t C = \frac{5}{3}

a c o t B + a + a c o t C = 36

\frac{47}{78} a + a + \frac{5}{3} a = 36 \Rightarrow 47 a + 78 a + 150 a = 2808

275 a = 2808

a = \frac{2808}{275} = 10.2