Angles of elevation

Question

Image of question

Hello i was wondering how would you calculate the height would it be

35xTan(29) or would you split up the angles in 2 and then add them up, also what are some alternative ways to do this.

Answer 1

$$AB=35\left(\tan17^{\circ}+\tan12^{\circ}\right)$$ and $$BC=\frac{35}{\cos17^{\circ}}$$

Answer 2

If $CAB$ were a right angle, then the answer would be $b * \tan (\theta + \phi$). But $CAB$ is not a right angle so this is not the case.

$CPB$ and $CPA$ are right angles so $PB = 35*\tan 17$ and $PA = 35*\tan 12$ so $AB = PA + PB = 35(\tan 17 + \tan 12)$.

If you had a different question: Say you and the tower are both on even ground and it is $35$ m to the base. Looking from the ground to the 2nd floor is an angle of $12$ and from where you stand the angle from the second floor to the top is $17$ then the answer would be: the height is $35 \tan(12+17)$.

But that is a different problem.