Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6 - Page 666: 30

Answer

The measure of length \[x\] is \[123\text{ units}\].

Work Step by Step

The trigonometric ratio for \[\text{Tangent }A\] will be determined by dividing the opposite side of angle A with the adjacent side of the triangle. To determine the length of \[x\], first compute the length of \[BC\] using the equation as shown below: In\[\vartriangle ABD\], we have \[\begin{align} & \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\ & =\frac{BD}{AD} \\ & \text{Tangent 40}{}^\circ =\frac{BD}{400} \end{align}\] \[\begin{align} & BD=\text{Tangent 40}{}^\circ \times 400 \\ & =0.8395\times 400 \\ & =336 \end{align}\] Now, compute the length of the CD using the equation as shown below: In\[\vartriangle ACD\], we have \[\begin{align} & \text{Tangent }A=\frac{\text{Opposite side of angle }A}{\text{Adjacent side of angle }A} \\ & =\frac{CD}{AD} \\ & \text{Tangent 28}{}^\circ =\frac{CD}{400} \end{align}\] \[\begin{align} & CD=\text{Tangent 28}{}^\circ \times 400 \\ & =0.5319\times 400 \\ & =213 \end{align}\] Now, as per the given figure \[\begin{align} & x=BC \\ & =BD-CD \\ & =336-213 \\ & =123 \end{align}\] Hence, the measure of length \[x\] is \[123\text{ units}\].
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