Question

The figure(in the attachment) drawn on graph paper shows triangle ABC with vertices A(-4,1) ,B(-4,6) and C(8,1).Now answer these questions below
1)Find length of BC
2) Find sin angle ABC and cos angle BCA
3) Find the area of ABC

Answer 1

Answer:

Refer attachment

Step-by-step explanation:

The area of triangle is in last the sin a and cos c is to the right and bc is at the top in the attachment

Answer 2

I) The length of BC = 13 units

II) sin(angle ABC) = 12/13 and cos(angle BCA) = 12/13

III) The area of triangle ABC = 30 sq. units

The three vertices of the triangle are A(-4,1) ,B(-4,6) and C(8,1).

Length of BC = √(144+25) = √169 = 13 units

Length of AC = √(144) = 12 units

Length of AB = √25 = 5 units

From the graph it is clear that the triangle ABC is a right angled triangle with angle BAC as 90°.

Sin(angle ABC) = AC/BC = 12/13

Cos(angle BCA) = AC/BC = 12/13

Area of the triangle ABC = (1/2) × AC × AB

= (1/2) × 12 × 5

= 30 sq. units