Given: ΔАВС, m∠ACB = 90°

m∠ACD = 30°
AD = 8 cm.
Find: CD, Perimeter of ΔABC

plz add answer

12=answer

Look How are both of u right?

Everyone Damon’s Forrest the answer is 48+16sgrt3

this is correct wth!H!1

To find CD and the perimeter of ΔABC, we can use trigonometry and the Pythagorean theorem.

First, let's analyze the given information:

1) ΔABC is a triangle.
2) ∠ACB is a right angle (90°).
3) ∠ACD is 30°.
4) AD = 8 cm.

Now, we can proceed to find CD and the perimeter of ΔABC:

Step 1: Finding CD
Since ∠ACB is a right angle, we can use the trigonometric relationship of the angles in a right triangle.

We know that CD is the side adjacent to the angle ∠ACD (which is 30°), and AD is the side opposite it. Thus, we can use the tangent function to find CD.

tan(30°) = CD / AD

Substituting the known values, we have:

tan(30°) = CD / 8

To find CD, we can solve for it:

CD = tan(30°) * 8
CD = 0.5774 * 8
CD = 4.6192 cm (rounded to four decimal places)

Therefore, CD is approximately 4.6192 cm.

Step 2: Finding the Perimeter of ΔABC
The perimeter of a triangle is the sum of the lengths of its sides. To find the perimeter of ΔABC, we need to calculate the lengths of all three sides.

We have already found the lengths of AD (8 cm) and CD (approximately 4.6192 cm). To find the remaining side, BC, we can use the Pythagorean theorem.

In the right triangle ΔABC, BC is the hypotenuse, AD is one of the legs, and CD is the other leg.

Using the Pythagorean theorem:

BC^2 = AD^2 + CD^2
BC^2 = (8^2) + (4.6192^2)
BC^2 = 64 + 21.3564
BC^2 = 85.3564
BC = √(85.3564)
BC = 9.236 cm (rounded to three decimal places)

Now that we have all three side lengths, we can calculate the perimeter:

Perimeter = AB + BC + AC
Perimeter = 8 + 9.236 + AC
Perimeter = 17.236 + AC

However, we still need to find the length of AC.

To find AC, we can use the Pythagorean theorem again:

AC^2 = AD^2 + CD^2
AC^2 = (8^2) + (4.6192^2)
AC^2 = 64 + 21.3564
AC^2 = 85.3564
AC = √(85.3564)
AC = 9.236 cm (rounded to three decimal places)

So, substituting this back into the perimeter equation:

Perimeter = 17.236 + 9.236
Perimeter = 26.472 cm (rounded to three decimal places)

Therefore, the perimeter of ΔABC is approximately 26.472 cm.

I assume D is on AB?

Is it an altitude hitting AB at 90deg ?

if so A is 60 and B is 30

then CD = 8 sqrt 3

AC = 16
AB = 32
BC = 16 sqrt 3
so perimeter = 48 + 16sqrt3

i got 77.9?

uglyy i say

yOu ugly trassh the answer is 12