Given triangle ABC with gamma = 61.0°, Beta = 29.0°, and b = 20.5, find the value of a.
A. 9.94
B. 11.4
C. 42.3
D. 37.0
Assuming angles α, β and γ are opposite to sides a, b and c respectively.
β=29°, γ=61°
=> α=180-(29+61)=90°
Since b and β are known, and both α and β are not obtuse, we can use the sine rule.
a/sin(α)=b/sin(β)
=>
a=b sin(α)/sin(β)