Question

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 .

Answer 1

Step-by-step explanation:

Using similarity it can be solved as:

$In\:\triangle PDW\: \& \: \triangle CTW\\\\\angle PDW \cong \angle CTW.... (each\:90 °) \\\\\angle PWD \cong \angle CWT... (Vertical\:\angle s) \\\\\therefore \triangle PDW\: \sim\: \triangle CTW\\(by \:AA\: criterion \: of\: similarity) \\\\\therefore \frac{PW}{CW} =\frac{WD}{WT}.. (csst) \\\\\therefore \frac{PW}{6} =\frac{12}{3}\\\\\therefore \frac{PW}{6} =4\\\\\therefore PW=4\times 6\\\\\huge \red {\boxed {\therefore PW=24}} \\\\In\:\triangle PDW\:, \angle PWD = 60°\\\\\therefore PD =\frac {\sqrt 3}{2} \times PW\\\\\therefore PD =\frac {\sqrt 3}{2} \times 24\\\\\huge \orange {\boxed {\therefore PD = 12\sqrt 3\: units}}$

Answer 2

Answer:

PD = 12$\sqrt{3}$

Step-by-step explanation:

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

tan30° = $\frac{1}{\sqrt{3} }$, then

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

PD = 12$\sqrt{3}$