What is the area of this triangle? enter your answer as a decimal. round only your final answer to the nearest tenth.

56.1 in^2

Step-by-step explanation:

When given sides "a" and "b" and the angle α between them, the applicable formula for the area of the triangle is ...

A = (1/2)ab·sin(α)

Substituting the given values, we find the area to be ...

A = (1/2)(14.2 in)(8 in)sin(99°) ≈ 56.1 in^2

56.1

Step-by-step explanation:

Diagram

Let's look at the diagram for a moment.

The 8 in line has been extended.

The dashed line is the height associated with the 8 inch line

The dashed line and the 8 inch line's extension meets at right angles.

Discussion

Normally you would take the 8 inch line and the height and divide their product by 2. You don't have the height. So you have to somehow get an expression for it.

The 81o angle is the supplement of the 99o angle. If you take the sine of both of them the sines are equal.

h = sin(81) * 14.2 because

sin(81) = opposite / hypotenuse.

opposite = hypotenuse * sin(81)

opposite = height = hypotenuse* sin(81)

height = 14.2 * sin(81)

Now we can find the area

Area

Area = height * base

base = 8

height = 14.2 * sin(81)

Area = 1/2 * 8 * 14.2 * sin(81)

Area = 56.1

answer: l

step-by-step explanation:

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕