16. What is the area of the triangle ABC if a=12, b=17, and B=35°?

Can anyone tell me the formula for this? Thank you!

A = (ab sinC)/2

so, how do you get C?

sinA/a = sinB/b
Now, having A and B, C is easy, since they add up to 180°

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

Area = (1/2)*base*height

However, to use this formula, we need to know the height of the triangle.

In this case, you are given two sides (a and b) and the angle between them (B). To find the height, we can use trigonometry.

To find the height, h, of the triangle, we can use the formula:

h = b*sin(B)

In this formula, b is the length of the side opposite to angle B, and sin(B) is the sine of angle B.

Now that we know the height, we can plug in the values into the formula:

Area = (1/2)*base*height = (1/2)*a*h

Substituting the given values:

Area = (1/2)*12*h

Area = 6h

To find the value of h, we substitute the values of b and B into the formula for height:

h = b*sin(B) = 17*sin(35°)

Using a calculator, we find:

h ≈ 9.86 (rounded to two decimal places)

Now, substituting this value of h back into the area formula:

Area = 6h = 6*9.86

Area ≈ 59.16 square units

Therefore, the area of triangle ABC is approximately 59.16 square units.