Kayla wants to find the width, AB, of a river. She walks along the edge of the river 75 ft and marks point C. Then she walks 35 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.

(a) Can Kayla conclude that Δ𝐴𝐵𝐶 and Δ𝐸𝐷𝐶 are similar?

Why or why not?

(b) Suppose DE = 21 ft. What can Kayla conclude about the width of the river?

upperclasspanda Jan 29, 2020

#1**+3 **

Yes they are similar triangles angle angle angle all three angles in each triangle are equal

Have you tried 'b' yet? ....similar triangles

ElectricPavlov Jan 29, 2020

#4

#5**+3 **

Since they are similar triangles, their sides are SIMILAR lengths....

One triangle has side length of 35 the other similar side in the OTHER triangle is 75 ft...

you can make a ratio of the side lengths 35 is to 75 35/75 is the ratio of similar sides in the two triangles

now they tell you DE is 21 feet.....and we are looking for the SIMILAR side in the other triangle, BA

these two sides will be in the same ratio 35/75

so you can say something like this 35 is to 75 as DE is to BA and we know DE is 21, so this looks like this:

35/75 = 21/BA now solve for BA ... can you do that now?

ElectricPavlov
Jan 29, 2020

#6**0 **

no, well... I don't know for sure ... I get what you're saying but I can't solve BA because if its similar wouldn't BA be considered 75? . . . I'm sorry, I'm not math smart.. .

upperclasspanda
Jan 30, 2020

#7**+2 **

'similar' doesn't mean 'exactly the same' ....just kind of alike....in a ratio

the triangles are similar....so sides in triangle edc are similar to sides in triangle abc ....in a ratio......not exactly the same...they are 'alike'

DC is similar to BC

ED is similar to AB (and EC is similar to AC....but we do not need this for this question)

DC is similar to BC as ED is similar to AB

35 is similar to 75 as 21 is similar to AB

35/75 = 21/AB

AB = 21/ (35/75)

AB = 21 * 75/35 Look at things and think about it for a while....it becomes easier....and intuitive after a while

ElectricPavlov
Jan 30, 2020