Question

f the measure of angle BCD is 67.4°, the measure of angle ABC is °. If the length of base AB is 80 feet, the length of DC is feet.

Answer 1

ABC= 112.6

DC= 105

Explanation:

got it right on edge!

Answer 2

`\angle ABC = 112.6^o`

`DE =105`

Explanation:

Given

See attachment for complete question

Required

`\angle ABC` and side length DC

Calculating
`\angle ABC`

First, calculate
`\angle EBC`

`\angle EBC + \angle BCE + 90 = 180` --- angles in a triang;e

`\angle BCE =\angle BCD = 67.4`

So:

`\angle EBC + 67.4+ 90 = 180`

`\angle EBC + 157.4 = 180`

Collect like terms

`\angle EBC = 180-157.4`

`\angle EBC = 22.6`

So:

`\angle ABC = \angle EBC +90`

`\angle ABC = 22.6 +90`

`\angle ABC = 112.6^o`

Calculating DC

First, calculate EC using Pythagoras theorem.

`BC^2 = BE^2 + EC^2`

`65^2 = 60^2 + EC^2`

`4225 = 3600 + EC^2`

Collect like terms

`EC^2 =4225 - 3600`

`EC^2 =625`

Take square roots

`EC = 25`

Length DC is:

`DC = DE + EC`

Where

`DE = AB =80`

So:

`DE =80+25`

`DE =105`