Chapter 8.2, Problem 3PSA

To determine

To calculate:The magnitude of angles $m\angle T\&m\angle S$ and the line segmentVT.

Answer to Problem 3PSA

Magnitudes of required angles: $m\angle T={90}^o\&m\angle S={30}^o$ and $VT=7.5\text{ units}$

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., $SV=15\text{ units},NV=20\text{ units},RP=10\text{ units},$

Formula used:

For given similar triangles

Angles are of same measure Sides are in same ratios

Calculation:

As per the definition of similar triangles,

In similar triangles, $\Delta NPR\sim \Delta STV$

  $\begin{array}{l}m\angle T=m\angle P=90°\\ m\angle S=m\angle N=30°\end{array}$

For finding VT , we have

  $\begin{array}{l}\frac{VT}{VS}=\frac{RP}{RN}\\ \Rightarrow \frac{VT}{15}=\frac{10}{20}\\ \Rightarrow VT=\frac{10}{20}\times 15\\ \Rightarrow VT==7.5units\end{array}$