Question

Darcy mounted a motion sensor so it would light a path to the door on her deck. If you know AB=10 feet, and BE and BD trident angle ABC, what is the perimeter of the deck area to the right of the beam of light ?PART 1: what others angles or sides of triangle BDC can you label given that side AB is 10 feet, BE and BD trisect angle ABC? Label the diagram accordingly, and explain your reasoning

Answer 1

Part 1

The labelled disgram is shown below.

We would apply the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

Considering triangle ABE

Sin 60 = 10/BE

BE = 10/Sin60 = 11.55

tan60 =10/AE

AE = 10/tan60 = 5.77

Part 1

Side DC of triangle BDC = 10 feet(opposite sides of a rectangle are congruent)

angle DBC = 30 degrees because BE and BD trisect angle ABC. 90/3 = 30

The sum of the angles in a triangle is 180 degrees. Thus,

angle DBC + angle DCB + angle BDC = 180

30 + 90 + angle BDC = 180

angle BDC = 180 = 180 - (30 + 90 = 180 - 120

angle BDC = 60

Sin 30 = CD/BD = 10/BD

BD = 10/Sin30

BD = 20

tan 30 = DC/BC = 10/BC

BC = 10/tan30

BC = 17.32

Perimeter of deck area to the right of the beam of light = perimeter of triangle BDC

= BD + DC + BC

= 20 + 10 + 17.32

Perimeter = 47.32 feet