find the area of each triangle to the nearest tenth.

in triangle YZX x=12cm z=16cm measure of angle Y= 130 degrees

in trianglE XYZ z= 11in. x= 7in. y= 13in.

Use this formula, which is attributed to Heron of Alexandria but can be traced back to Archimedes.

Area = sqrt[s(s-a)(s-b)(s-c)],

where s=(a+b+c)/2 or perimeter/2.

To use that formula on the first triangle, you need to figure the length of side y

Draw the altitude h from Y to XZ, meeting XZ at P
Let angle a = <XYP

h/16 = cos a
h/12 = cos(130-a)

16cos z = 12cos(130-a)
a = 68.81°

So, side y = XZ = 16sin68.81° + 12sin61.19° = 25.432

Now you can use Heron's formula to find the area: 73.54

To find the area of a triangle, you can use the formula:

Area = (1/2) * base * height.

For the first triangle, triangle YZX, you have the information about the lengths of two sides (x = 12 cm and z = 16 cm) and the measure of angle Y (130 degrees). However, to calculate the area, you need the height of the triangle.

To find the height, you can use trigonometric functions. Since you have the angle and the opposite side, you can use the sine function, which is defined as:

sin(angle) = opposite / hypotenuse.

In this case, the opposite side is the height of the triangle, and the hypotenuse is side z. So, you can rearrange the formula to solve for the height:

height = hypotenuse * sin(angle).

Plugging in the values we have:

height = 16 cm * sin(130 degrees).

Now, you can calculate the height, and once you have the height, you can use it along with the base to find the area.

For the second triangle, triangle XYZ, you have the information about all three sides (x = 7 in, y = 13 in, and z = 11 in). To find the area, you can again use the formula:

Area = (1/2) * base * height.

In this case, you have the lengths of all three sides, so you can use Heron's formula to calculate the area without needing to find the height explicitly. Heron's formula is defined as:

Area = sqrt(s * (s - a) * (s - b) * (s - c)),

where s is the semi-perimeter of the triangle calculated as:

s = (a + b + c) / 2,

and a, b, and c are the lengths of the three sides.

Plugging in the given values:

s = (7 in + 11 in + 13 in) / 2,

Once you have the value of s, you can substitute it into Heron's formula to find the area of the triangle XYZ.