Chose the missing side length and the trigonometric ratio you would use to calculate.

The missing value is 2.9mm and cosine was used

Step-by-step explanation:

Given triangle is a right-angled triangle  we can use trigonometric ratios to calculate the missing length.

In the given triangle,

Base = k

Hypotenuse = 15mm

Angle = 79

We will use trigonometric ratio which includes base and hypotenuse.

Using cosine,

Rounding off to nearest tenth

Hence,

The missing value is 2.9mm and cosine was used

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the answer is. -82562234434584

step-by-step explanation: