Question

How do you solve \[\tan \left( 55 \right)=\dfrac{c+4}{c}\] ?

Answer 1

Hint: In this problem, we have to solve the given trigonometric expression and find the value of c. We can first multiply c on both sides of the given expression, and cancel similar terms. We can then subtract c on both the sides of the equation and cancel similar terms, we can simplify the terms similarly to get the value of x.

Complete step by step answer:
We know that the given trigonometric expression to be solved is,
\[\tan \left( 55 \right)=\dfrac{c+4}{c}\].
Now we can multiply c on both the left-hand side and the right-hand side of the expression, we get
\[\Rightarrow \tan \left( 55 \right)\times c=\dfrac{c+4}{c}\times c\]
Now we can cancel, the same numerator and the denominator in the above expression.
\[\Rightarrow c\tan \left( 55 \right)=c+4\]
Now we can add -c on both the left-hand side and the right-hand side of the expression, we get
\[\Rightarrow c\tan \left( 55 \right)-c=c+4-c\].
Now we can take the common term c from the left-hand side, we get
\[\Rightarrow c\left( \tan \left( 55 \right)-1 \right)=4\]
Now we can divide by \[\left( \tan \left( 55 \right)-1 \right)\] on both the left-hand side and the right-hand side of the expression, we get
\[\Rightarrow \dfrac{c\left( \tan \left( 55 \right)-1 \right)}{\left( \tan \left( 55 \right)-1 \right)}=\dfrac{4}{\left( \tan \left( 55 \right)-1 \right)}\]
Now we can cancel the similar terms in the above step, we get
\[\Rightarrow c=\dfrac{4}{\tan \left( 55 \right)-1}\]
Therefore, the value of \[c=\dfrac{4}{\tan \left( 55 \right)-1}\].

Note:
Students make mistakes while simplifying the given trigonometric equation, which should be concentrated. We can also convert the tan values into exact values, if needed or if asked. To solve these types of problems, we may have to know some trigonometric formulas, identities and degree values to get an exact answer for the respective problem.