Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

To indirectly measure the distance across a lake, Nachelle makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter

To Indirectly Measure The Distance Across A Lake Nachelle Makes Use Of A Couple Landmarks At Points D And E She Measures CF FD And FG As Marked Find The Distanc class=

Sagot :

asuwafohjames

Answer:

207.68 m

Step-by-step explanation:

From the diagram,

ΔDEC is similar to ΔFGC

Therefore,

(DE)/(FG) = (DC)/(FC).............. Equation 1

make line DE the subject of the equation

DE = [(DC)(FG)/(FC)]................ Equation 2

From the diagram,

Given: DC = 190 m, FG = 142.1 m, FC = 130 m

Substitute these values into equation 2

DE = (190×142.1/130)

DE = 207.68 m

Hence the distance across the lake is 207.68 m

akposevictor

Applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m

Recall:

  • The corresponding side lengths of two triangles that are similar are always proportional to each other.

Thus:

ΔCDE  and ΔCFG are similar to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore:

DE/FG = DC/FC

  • Substitute

DE/142.1 = 190/130

  • Cross multiply

[tex]DE = \frac{190 \times 142.1}{130} \\\\\mathbf{DE = 207.68 $ m}[/tex] (nearest hundredth).

Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m

Learn more about similar triangles here: https://brainly.com/question/11899908

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.