Question

It is not an graded assignment or anything else that is graded

Answer 1

The answer is B.

`x=(c)/(1+(\tan\beta)/(\tan\theta))`

EXPLANATION :

Note that the tangent of an angle is :

`\tan\theta=(opposite)/(adjacent)`

For angle B :

`\begin{gathered} \tan\theta=(h)/(c-x) \\ h=(c-x)\tan\theta \end{gathered}`

For angle A :

`\begin{gathered} \tan\beta=(h)/(x) \\ h=x\tan\beta \end{gathered}`

Equate both functions in h :

`\begin{gathered} h=h \\ (c-x)\tan\theta=x\tan\beta \\ c\tan\theta-x\tan\theta=x\tan\beta \\ c\tan\theta=x\tan\theta+x\tan\beta \\ c\tan\theta=x(\tan\theta+\tan\beta) \\ x=(c\tan\theta)/(\tan\theta+\tan\beta) \\ \text{ Multiply the numerator and denominator by 1 over tan \lparen theta\rparen :} \\ x=(c\tan\theta*(1)/(\tan\theta))/((\tan\theta+\tan\beta)*(1)/(\tan\theta)) \\ x=(c)/(1+(\tan\beta)/(\tan\theta)) \end{gathered}`