Question

question 20
5 pts
find the area of the triangle. round intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your final answer to the nearest tenth.
area=

Explanation:

Step1: Find height of triangle

Let the height be $h$. In the right - triangle on the right side with angle $44^{\circ}$ and base $x$. We know that $\tan44^{\circ}=\frac{h}{x}$. Also, in the left - hand right - triangle with angle $70^{\circ}$ and base $46 - x$. So $\tan70^{\circ}=\frac{h}{46 - x}$.
From $\tan44^{\circ}=\frac{h}{x}$, we have $x = \frac{h}{\tan44^{\circ}}\approx\frac{h}{0.966}$. From $\tan70^{\circ}=\frac{h}{46 - x}$, we have $46 - x=\frac{h}{\tan70^{\circ}}\approx\frac{h}{2.747}$.
Substitute $x=\frac{h}{0.966}$ into $46 - x=\frac{h}{2.747}$, we get $46-\frac{h}{0.966}=\frac{h}{2.747}$.
$46=\frac{h}{0.966}+\frac{h}{2.747}$.
$46 = h(\frac{1}{0.966}+\frac{1}{2.747})$.
$46 = h(\frac{2.747 + 0.966}{0.966\times2.747})$.
$46 = h(\frac{3.713}{2.654})$.
$h=\frac{46\times2.654}{3.713}\approx32.9$.

Step2: Calculate area of triangle

The area of a triangle $A=\frac{1}{2}\times base\times height$. Here the base is $46$ and height $h\approx32.9$.
$A=\frac{1}{2}\times46\times32.9 = 495.4$.

Answer:

495.4