Question

First correct answer will be brainliest marked.

Answer 1

Answer:

8.1 cm

Step-by-step explanation:

Find BD from right Δ ABD, using Pythagoras Theorem

$BD = \sqrt{(7.5^{2})+5^{2} } = \sqrt{81.25} = 9.01 cm$

Draw a perpendicular from point B towards side DC, say meeting at E

Then, sin 38° = BE/BD

or BE = BD sin 38° = 9.01 × 0.615 = 5.547 cm

Now, cos 38° = DE/BD

or DE = BD cos 38° = 9.01 × 0.788 = 7.099 cm

Now, CE = CD - DE = 13 - 7.099 = 5.9 cm

In Δ BEC,

$BC = \sqrt{(BE^{2})+EC^{2} }$

$BC = \sqrt{(5.547^{2})+5.9^{2} } = \sqrt{65.58} = 8.1 cm$