Question

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

Answer 1

Answer:

Option C. $BC=31.2\ units$

Step-by-step 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

$m$

$sin($ -------> equation A

step 3

In the right triangle ABC

$sin($ ------> equation B

Remember that

$m$

so equate equation A and equation B solve for DC

$\frac{5}{13}=\frac{13}{5+DC}$

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

$25+5DC=169$

$5DC=169-25$

$5DC=144$

$DC=144/5=28.8\ units$

step 4

In the right triangle BDC find the length side BC

Applying the Pythagoras Theorem

$BC^{2}=28.8^{2}+12^{2}$

$BC^{2}=973.44$

$BC=31.2\ units$

Answer 2

The answer is C.31.2 HOPE IT HELPS