Answer:
Step-by-step explanation:
Given
We know that trigonometric ratio as
- sin Ф = opposite/hypotenuse
- cos Ф = adjacent/hypotenuse
- tan Ф = opposite/adjacent
as
sin A = sin 40 = opposite/hypotenuse
From the diagram, it is clear that the opposite of angle A is a=8 and the hypotenuse is 'c'.
also the angle
sin A = sin 40 = opposite/hypotenuse = a/c = 8/c
sin 40 = 8/c
c = 8/sin 40
c = 8/0.745
c = 10.7
so the value of c will be: 10.7 units
so
tan B = opposite/adjacent
= b/a
= 0.9
[tex]B=\tan ^{-1}\left(0.9\right)[/tex]
[tex]=42^{\circ \:}[/tex]
Therefore, the value of B = [tex]42^{\circ \:}[/tex]
As the sum of the angles of triangle ABC is 180.
i.e.
A+B+C = 180
(40)° + (42)° + C = 180°
C = 180° - 40° - 42°
= 98°
Therefore, the value of C = 98°
Hence,
