Question

For the following question, find the area of the triangle. give the answer to the nearest tenth. The drawing may not be to scale

Answer 1

Option B

`63.4 cm^2`

Explanation:

The area of a triangle is half the product of its base by the height.

`A = 0.5bh`

Where b is the base and h is the height.

In this triangle
`b = 9\ cm`.

The height of this triangle is a line perpendicular to its base that goes to the vertex opposite the base.

We do not know this length. But this line h divides the triangle into two rectangular triangles.

So for this triangle the opposite side at the 70 ° angle is h.

Therefore we know that senx is defined as:

`senx = (opposite\ side)/(hypotenuse)`

Where:

Opposite side = h

hypotenuse = 15 cm

x = 70°

`sin(70) = (h)/(15)`

`h = sin(70)(15)`

`h = 14.09 cm`

Finally, the area is:

`A = 0.5(14.09)(9)\\A = 63.4 cm ^ 2`