Question

1) complete the special right triangle what is length of BD what is length of BC

Answer 1

Answer:

$BD = 4$

$BC =4\sqrt 3$

Step-by-step explanation:

Given

The attached triangle

Required

Find BD and BC

Solving BD

Considering angle at D, we have:

$\cos(D) = \frac{Adjacent}{Hypotenuse}$

$\cos(60) = \frac{BD}{8}$

Solve for BD

$BD = 8 * \cos(60)$

$\cos(60) = 0.5$ So:

$BD = 8 * 0.5$

$BD = 4$

To solve for BC, we make use of Pythagoras theorem

$CD^2 = BC^2 + BD^2$

This gives

$8^2 = BC^2 + 4^2$

$64 = BC^2 + 16$

Collect like terms

$BC^2 =64-16$

$BC^2 =48$

Take square roots

$BC =\sqrt{48$

Expand

$BC =\sqrt{16*3$

Split

$BC =\sqrt{16}*\sqrt 3$

$BC =4\sqrt 3$