Question

Sejam dois ângulos a e b, tais que sen a : 3/5, cos a : 4/5, sen b: 5/13 e cos b : 12/13.
Quanto vale sen( a + b)?

a) 56/65.
b) 57/65.
c) 58/65.
d) 59/65.
e) 61/65.​

Answer 1

Explicação passo-a-passo:

$\sf sen~(a+b)=sen~a\cdot cos~b+sen~b\cdot cos~a$

$\sf sen~(a+b)=\dfrac{3}{5}\cdot\dfrac{12}{13}+\dfrac{5}{13}\cdot\dfrac{4}{5}$

$\sf sen~(a+b)=\dfrac{36}{65}+\dfrac{20}{65}$

$\sf sen~(a+b)=\dfrac{36+20}{65}$

$\sf sen~(a+b)=\dfrac{56}{65}$

Letra A