Question

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

___in^2

Answer 1

Answer:

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

Answer 2

Answer:

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