Question

question 19
5 pts
find the length of the side labeled x. round intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your final answer to the nearest tenth.
9
x
x=

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is $180^{\circ}$. Let the third angle be $\theta$. So $\theta=180-(90 + 35+51)=4^{\circ}$.

Step2: Use the tangent function

We know that $\tan35^{\circ}=\frac{h}{9}$, where $h$ is the height of the large right - triangle. So $h = 9\times\tan35^{\circ}\approx9\times0.700\approx6.3$.

Step3: Use the tangent function for the larger triangle

We also know that $\tan(35 + 51)^{\circ}=\tan86^{\circ}=\frac{h}{9 - x}$. Since $\tan86^{\circ}\approx14.301$ and $h\approx6.3$, we have $14.301=\frac{6.3}{9 - x}$.
Cross - multiply: $14.301\times(9 - x)=6.3$.
$128.709-14.301x = 6.3$.
$14.301x=128.709 - 6.3$.
$14.301x = 122.409$.
$x=\frac{122.409}{14.301}\approx13.5$.

Answer:

$13.5$