Given: ABCD is a rectangle, AC∩BD = O, m∠ABD = 30°, AC = 16 in. Find BC.

Question

What is the length of BC?

Answer 1

Its helpful to draw a picture.

Label a triangle with pts 

A.        D

.

.

.C.       B

 

the first part says AC is parallel to BD

The second thing says AC = 16 in which means BD = 16 inches since opposite sidrs of rectangle are same

 

We are given angle ABD = 30 degrees and asked to find BC. We can find AD which will be same.

 

We know tan30 = opp/adj = AD/BD = AD/16

So AD = 16tan30

Tan30 = sin30/cos30 = (1/2)/*sqr(3/2) = 1/sqr(3) = sqr(3)/3 (remember unit circle)

 

Thus AD= 16sqr(3)/3

 

Alternativel since ABD = 30 that means ABC = 60 and tan60 = AC/BC = 16/BC 

So BC = 16/tan60

Tan60 =  sin60/cis60 = (sqr(3)/2)/(1/2) = sqr(3)

So BC = 16/sqr(3) = 16sqr(3)/3

 

Best - david