find the area of the given triangle. round your answer to the nearest tenth. do not round any intermediate…

Explanation:

Step1: Find the other side adjacent to the right - angle

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 54^{\circ}$ and the side adjacent to $54^{\circ}$ (opposite to the right - angle) is $a = 19$. Let the other side adjacent to the right - angle be $b$. Then $\tan54^{\circ}=\frac{b}{19}$, so $b = 19\tan54^{\circ}$.

Step2: Use the area formula for a right - triangle

The area formula for a right - triangle is $A=\frac{1}{2}ab$. Substituting $a = 19$ and $b = 19\tan54^{\circ}$ into the formula, we get $A=\frac{1}{2}\times19\times19\tan54^{\circ}$. We know that $\tan54^{\circ}\approx1.37638$. Then $A=\frac{1}{2}\times19\times19\times1.37638$. $A=\frac{1}{2}\times19\times19\times1.37638=\frac{1}{2}\times361\times1.37638 = 180.5\times1.37638\approx248.4$.

Answer:

$248.4$ square units