Answer:
The length of the third side is
[tex]c =8.82 \ m [/tex]
The tangent of the angle for which 6.9 m is the opposite side is
[tex]k = 1.256[/tex]
Explanation:
From the question we are told that
The first side is a = 6.9 m
The second side is b = 5.5 m
Generally apply Pythagoras theorem
[tex]c^2 = a^2 + b^2[/tex]
=> [tex]c = \sqrt{a^2 + b^2 }[/tex]
=> [tex]c = \sqrt{6.9^2 + 5.5^2 }[/tex]
=> [tex]c =8.82 \ m [/tex]
From sin rule we have that
[tex]\frac{c}{sin(\theta )} = \frac{a}{sin (\beta )}[/tex]
Generally from a right triangle the angle [tex]\theta = 90[/tex]
So
[tex]\frac{8.82}{sin(90 )} = \frac{6.9}{sin (\beta )}[/tex]
=> [tex]\beta = sin ^{-1}[\frac{6.9}{8.82} ][/tex]
=> [tex]\beta =51.47^o[/tex]
Generally the tangent of the angle for which 6.9 m is the opposite side is mathematically represented as
[tex]k = tan (\beta )[/tex]
[tex]k = tan (51.47 )[/tex]
[tex]k = 1.256[/tex]
