Chapter 4.5, Problem 5CYU

(a)

To determine

To explain:

The use of triangles to estimate value of $AB$

Answer to Problem 5CYU

The distance between $A$ and $B$ can be estimated by measuring $\overline{DC}$

Explanation of Solution

Given information:

  $\begin{array}{l}\overline{CA}\perp \overline{AB}\\ \overline{CD}\perp \overline{CA}\end{array}$

  

Since $\angle BAE$ and $\angle DCE$ are right angles, therefore $\angle BAE\cong \angle DCE$ .

According to the mid-point theorem:

  $\overline{AE}\cong \overline{EC}$

According to the vertical angles theorem:

  $\angle DEC\cong \angle BEA$

Surveyor knows that the angle side angle (ASA) congruence postulate to get:

  $\Delta DCE\cong \Delta BAE$

Know that:

The corresponding parts of congruent triangles are congruent so,

  $\overline{DC}\cong \overline{AB}$

Therefore, surveyor can measure $\overline{DC}$ and get the distance between $A$ and $B$

(b)

To determine

To calculate:

The value of $AB$

Answer to Problem 5CYU

The value of $AB$ is $550m$

Explanation of Solution

Given information:

  $\begin{array}{l}DC=550m\\ \overline{DC}\cong \overline{AB}\end{array}$

From sub-part (a):

  $\overline{DC}\cong \overline{AB}$

Since $DC\text{}=550m$ , use the definition of the congruence to get the value of $AB$ :

  $AB=DC\text{}=550m$