Question

What is the length of BC, rounded to the nearest tenth?

A. 13.0 units
B. 28.8 units
C. 31.2 units
D. 33.8 units

Answer 1

The answer is C.31.2 HOPE IT HELPS

Answer 2

Option C.
`BC=31.2\ units`

Explanation:

step 1

In the right triangle ABD find the length side AB

Applying the Pythagoras Theorem

`AB^(2)=5^(2)+12^(2)`

`AB^(2)=169`

`AB=13\ units`

step 2

In the right triangle ABD

we know that

`m<ABD=m<BCD`

`sin(<ABD)=(5)/(13)` -------> equation A

step 3

In the right triangle ABC

`sin(<BCD)=(13)/(5+DC)` ------> equation B

Remember that

`m<ABD=m<BCD`

so equate equation A and equation B solve for DC

`(5)/(13)=(13)/(5+DC)`

`5(5+DC)=13*13`

`25+5DC=169`

`5DC=169-25`

`5DC=144`

`DC=144/5=28.8\ units`

step 4

In the right triangle BDC find the length side BC

Applying the Pythagoras Theorem

`BC^(2)=28.8^(2)+12^(2)`

`BC^(2)=973.44`

`BC=31.2\ units`