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In the figure below, PDW and WTC are right triangles. The measure of WPD is 30°, the measure of WC is 6 units, the measure of WT is 3 units, and the measure of WD is 12 units. Determine the measure of PD .

In the figure below PDW and WTC are right triangles The measure of WPD is 30 the measure of WC is 6 units the measure of WT is 3 units and the measure of WD is class=

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Answer:

PD = 12[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the tangent ratio in right Δ PDW and the exact value

tan30° = [tex]\frac{1}{\sqrt{3} }[/tex], then

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{WD}{PD}[/tex] = [tex]\frac{12}{PD}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

PD = 12[tex]\sqrt{3}[/tex]

Hrishii

Step-by-step explanation:

Using similarity it can be solved as:

[tex] In\:\triangle PDW\: \& \: \triangle CTW\\\\

\angle PDW \cong \angle CTW.... (each\:90 °) \\\\

\angle PWD \cong \angle CWT... (Vertical\:\angle s) \\\\

\therefore \triangle PDW\: \sim\: \triangle CTW\\

(by \:AA\: criterion \: of\: similarity) \\\\

\therefore \frac{PW}{CW} =\frac{WD}{WT}.. (csst) \\\\

\therefore \frac{PW}{6} =\frac{12}{3}\\\\

\therefore \frac{PW}{6} =4\\\\

\therefore PW=4\times 6\\\\

\huge \red {\boxed {\therefore PW=24}} \\\\

In\:\triangle PDW\:, \angle PWD = 60°\\\\

\therefore PD =\frac {\sqrt 3}{2} \times PW\\\\

\therefore PD =\frac {\sqrt 3}{2} \times 24\\\\

\huge \orange {\boxed {\therefore PD = 12\sqrt 3\: units}} [/tex]

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