In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C. A.60^@ B.90^@ C.120^@ D.150^@

potrzebag18

potrzebag18

Answered question

2023-02-09

In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.
A. 60
B. 90
C. 120
D. 150

Answer & Explanation

Stephany Horn

Stephany Horn

Beginner2023-02-10Added 6 answers

We know from trigonometric ratios of half angles that tan A 2 = ( s b ) ( s c ) ( s a ) ( s )
Here we need angle opposite to c i.e., C.
Semiperimeter, S = a + b + c 2 = 3 + 5 + 7 2 = 15 2
tan C 2 = ( s b ) ( s a ) ( s c ) ( s )
= ( s 3 ) ( s 5 ) ( s 7 ) s = ( 15 6 ) ( 15 10 ) ( 2 ) 4 ( 15 14 ) ( 15 2 )
= 9 ( 5 ) 15 = 3 C 2 = 60 C = 120

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