Sarah, who is 1.72 m tall, wishes to find the height of a tree. She walks 18.77 m from the base of the tree along the shadow of the tree until her head is
in a position where the tip of her shadow exactly overlaps the end of the
tree top's shadow. She is now 5.38 m from the end of the shadows. How
tall is the tree? Round to the nearest hundredth. *

7.7 m

Step-by-step explanation:

let's give the tree height T

T = 1.72 × (18.77+5.38)/5.38

T = 1.72 × 24.15/5.38

T = 41.538/5.38

T ≈ 7.7 m

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.