Question

A park ranger is shining a spotlight to try to count wildlife at night. She

starts with a beam that has an angle of 45°. She then increases the angle
of the beam to 60°.
Which statement most accurately describes the relationship between
segments of the triangles formed by the beam?​

Answer 1

The statement most accurately describes the relationship between

segments of the triangles formed by the beam is AC < DF

Explanation:

* Lets study the figure to answer the problem

- There are two triangles ABC and DEF

- AB = BC

- DE = EF

- AB = DE

∴ AB = BC = DE = EF

- m∠ABC = 45°

- m∠DEF = 60°

∵ The measure of angle ABC is smaller than the measure of

angle DEF

∴ The opposite side to the angle ABC is shorter than the opposite

side of angle DEF

∵ AC is the opposite side to angle ABC

∵ DF is the opposite side to angle DEF

∴ AC is shorter than DF

∴ DF > AC

∴ AC < DF

* The statement most accurately describes the relationship between

segments of the triangles formed by the beam is AC < DF