Question

Given: ΔАВС, m∠ACB = 90° CD ⊥ AB, m∠ACD = 60° BC = 6 cm. Find: АD

Answer 1

Since bc = 6, that makes db = 3 and cd = 3rad3
cd (2) = ac. so ac = 6rad3
so to get ad, you square ac which = 108, square cd which = 3rad3 which equals 27. 108 - 27 = 81. the sqaure root of 81 is 9. ad = 9

Answer 2

Answer:

$AD=9\ cm$

Step-by-step explanation:

Step 1

In the right triangle BCD

Find  the measure of CD

we know that

m∠DCB = $90\°-60\°=30\°$

$cos(30\°)=\frac{CD}{BC}$

$cos(30\°)=\frac{\sqrt{3}}{2}$

so

$\frac{CD}{BC}=\frac{\sqrt{3}}{2}$

solve for CD

$CD=BC\frac{\sqrt{3}}{2}$

we have

$BC=6\ cm$

substitute

$CD=(6)\frac{\sqrt{3}}{2}$

$CD=3\sqrt{3}\ cm$

Step 2

In the right triangle ACD

Find  the measure of AD

we know that

$tan(60\°)=\frac{AD}{CD}$

$tan(60\°)=\sqrt{3}$

so

$\frac{AD}{CD}=\sqrt{3}$

solve for AD

$AD=(CD)\sqrt{3}$

we have

$CD=3\sqrt{3}\ cm$

substitute

$AD=(3\sqrt{3})\sqrt{3}=9\ cm$

$AD=9\ cm$