Chapter 6.5, Problem 12E

a.

To determine

The height of the girl in feet

Answer to Problem 12E

The girl’s height in feet is 5.25 feet

Explanation of Solution

Given:

Girl’s height $=5ft\text{ 3}in$

Calculation:

  $\text{3 }in=0.25ft$

Therefore , girl’s height $=$$\text{5}ft+0.25ft=5.25ft$

Conclusion:

Girl’s height is 5.25 feet.

b.

To determine

To write and solve the proportional to find the height of the rock in feet and inches

Answer to Problem 12E

Height of the rock in is 15feet and 9 inches

Explanation of Solution

Given:

Let the rock make a triangle DEF by the shadow it casts on the ground.

Let the girl make a triangle ABC by the shadow she casts on the ground.

DE $=h\text{ EF=21 }ft\text{ FD=}x\text{ BC=7 }ft\text{ AB=5}\text{.25 }ft$

And $\Delta ABC\sim \Delta DEF$

Calculation:

Since both the triangles are similar, then the ratio of their corresponding sides will also be proportional,

  $\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}$ ,

  $\frac{5.25}{h}=\frac{7}{21}$

  $h=\frac{21\times 5.25}{7}$

  $h=15.75ft\text{or 15}ft\text{ and 9}inches$

Conclusion:

.Height of the rock in is 15feet and 9 inches