Chapter 8.5, Problem 14WE

To determine

To find the values of $w$ and $z$

Answer to Problem 14WE

$w\approx 286$ and $z\approx 571$

Explanation of Solution

Given information:

Right angle triangles

It can be observed that two triangles are congruent by the postulate SAS.

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$\Rightarrow$ The corresponding lengths are equal.

Thus, base $=w$ and perpendicular $=200$

  $\begin{array}{l}\Rightarrow \cos 35=\frac{\text{perpendicular}}{\text{base}}\\ \Rightarrow \tan 35=\frac{200}{w}\\ \Rightarrow w=\frac{\left(200\right)}{\tan 35}\\ \Rightarrow w=\frac{\left(200\right)}{\left(0.70021\right)}\\ \Rightarrow w=285.6296\\ \therefore w\approx 286\end{array}$

  $\begin{array}{l}\Rightarrow z=2w\\ =2\left(285.6\right)\\ =571.259\\ \therefore z\approx 571\end{array}$

Hence, $w\approx 286$ and $z\approx 571$