Question

1. 15° 33 x

Explanation:

Step1: Identify the trigonometric relation

We know that in a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 15^{\circ}$ and the adjacent side to the angle $\theta$ is 33 and the hypotenuse is $x$.
So, $\cos15^{\circ}=\frac{33}{x}$.

Step2: Solve for $x$

We know that $\cos15^{\circ}=\cos(45^{\circ}- 30^{\circ})=\cos45^{\circ}\cos30^{\circ}+\sin45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}\approx0.9659$.
From $\cos15^{\circ}=\frac{33}{x}$, we can rewrite it as $x = \frac{33}{\cos15^{\circ}}$.
Substitute the value of $\cos15^{\circ}$: $x=\frac{33}{0.9659}\approx34.27$.

Answer:

$x\approx34.27$