Question

find the length x to the nearest whole number.
(do not round until the final answer. then round to the nearest whole number.)

Explanation:

Step1: Use tangent function for upper - triangle

Let's consider the upper right - triangle with angle $43^{\circ}$ and adjacent side length $450$. The tangent of an angle $\theta$ in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For the upper triangle with $\theta = 43^{\circ}$ and adjacent side $a = 450$, the length of the upper part of $x$ (let's call it $y$) is given by $y = 450\times\tan43^{\circ}$.

Step2: Use tangent function for lower - triangle

Now consider the lower right - triangle with angle $22^{\circ}$ and adjacent side length $450$. The length of the lower part of $x$ (let's call it $z$) is given by $z = 450\times\tan22^{\circ}$.

Step3: Calculate $x$

$x=y + z=450\times\tan43^{\circ}+450\times\tan22^{\circ}$.
We know that $\tan43^{\circ}\approx0.9325$ and $\tan22^{\circ}\approx0.4040$.
So $x = 450\times0.9325+450\times0.4040=450\times(0.9325 + 0.4040)=450\times1.3365 = 601.425$.

Answer:

$601$