Chapter 8.2, Problem 19PSC

To determine

To calculate:The length of the line segment ST and NP.

Answer to Problem 19PSC

The length of ST = 12.75 units

The length of NP = 1.7 units

Explanation of Solution

Given information Triangles are similar, i.e. $\Delta NPR\sim \Delta STV$

Magnitude of angles, i.e., $m\angle P=90°,m\angle R=60°$

Magnitude of line segments, i.e., $SV\text{=15 units, }NV\text{=20 units,}RP\text{=10 units,}$

Formula used For given similar triangles

Angles are of same measure Sides are in same ratios

Pythagoras theorem

Calculation

In $\Delta SVT$ , we have

  $\begin{array}{l}ST\\ =\sqrt{{\left(SV\right)}^2-{\left(VT\right)}^2}\\ =\sqrt{{\left(15\right)}^2-{\left(7.5\right)}^2}\\ =7.5\sqrt{3}\\ =7.5\times 1.7\\ =12.75units\end{array}$

Further, we have

  $\begin{array}{l}\frac{NP}{ST}=\frac{RN}{SV}\\ \Rightarrow \frac{NP}{7.5\sqrt{3}}=\frac{20}{15}\\ \Rightarrow NP=10\sqrt{3}=10\times 1.7=17\text{ units}\end{array}$