Question

In a school hall, the stage is lit by a spotlight fixed to a wall. The spotlight is 4.35 metres up the wall and is set to shine on a spot on the stage 5.2 metres away from the wall, as shown in the diagram. Calculate the size of the angle marked x${}^{\circ }$.

• A. 50${}^{\circ }$.
• B. 45${}^{\circ }$.
• C. 35${}^{\circ }$.
• D. 30${}^{\circ }$.

Answer 1

The correct option is A 50${}^{\circ }$.

$tanx=\frac{5.2}{4.35}=1.195\Rightarrow x=50.08=50.1$ or $50$
Some students may feel they do not know $\tan \theta$ value for angle ${50}^{\circ }$.

The options do not require that you remember the value, as the value of $\tan x$ is greater than 1.

Angle $x$ must be greater than ${45}^{\circ }$