A right triangle is shown above where and Line segments are continually drawn to be

Chapter 9, Problem 112

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Length A right triangle XYZ is shown above where \(|X Y|=z\) and \(\angle X=\theta\). Line segments are continually drawn to be perpendicular to the triangle, as shown in the figure.

(a) Find the total length of the perpendicular line segments \(\left|Y y_{1}\right|+\left|x_{1} y_{1}\right|+\left|x_{1} y_{2}\right|+\cdots\) in terms of z and \(\theta \text {. }\)

(b) If \(z=1\) and \(\theta=\pi / 6\), find the total length of the perpendicular line segments.

Text Transcription:

|X Y|=z

angleX=theta

|Yy_1|+|x_1y_1|+|x_1y_2+cdots

theta

z=1

theta=pi/6

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