Given: δавс, m∠acb = 90° cd ⊥ ab , m∠acd = 30°,ad = 8 cm find: perimeter of δabc

Perimeter of is .

Explanation:

Given: In , ,  and AD= 8cm.

In

Sum of the measure of the angles of triangles is 180 degree.

or

Simplify:

∵ AD= 8cm and   to calculate the length of CD we use tangent ratio i.e,

then;

or

Simplify:

cm.

Also, find the length of AC, we use sine ratio i.e, .

Then,

or

On simplify:

cm.

Now, in triangle ABC;

, then

    [Sum of the measure of the angles in the triangle is 180 degree]

To calculate the length of BC;

    [∴ ]

therefore,

or

Simplify:

cm.

Using Pythagoras theorem in triangle ACB;

Let BD be x cm

AB = 8+x cm ,  AC = 16 cm and cm

or

or

Simplify:

x=24 cm

Therefore, the length of AB = 8+x= 8+24=32 cm

Perimeter(P) of triangle ABC is equal to the sum of the sides of the triangle.

⇒ P= AB+BC+AC = cm

the answer

b. they are parallel and will never intersect.