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 larger triangle

Let the height of the larger right - triangle be $h_1$. We know that $\tan(25^{\circ})=\frac{h_1}{580}$, so $h_1 = 580\times\tan(25^{\circ})$.

Step2: Use tangent function for smaller triangle

Let the height of the smaller right - triangle be $h_2$. We know that $\tan(21^{\circ})=\frac{h_2}{580}$, so $h_2 = 580\times\tan(21^{\circ})$.

Step3: Calculate the value of $x$

$x=h_1 - h_2=580\times\tan(25^{\circ})-580\times\tan(21^{\circ})$.
We know that $\tan(25^{\circ})\approx0.4663$ and $\tan(21^{\circ})\approx0.3839$.
$x = 580\times(0.4663 - 0.3839)=580\times0.0824$.
$x=580\times0.0824 = 47.792$.

Answer:

48