We can calculate the area of a triangle by means of the following formula:
[tex]A=\frac{b\times h}{2}[/tex]
Where b is the length of the base and h is the height of the triangle.
The height of the triangle is a segment that goes from the top vertex to its base, like this:
As you can see in the above figure, the inscribed triangle on the right side is a right triangle, then we can apply the function sin(θ) in order to calculate the length of the side h, like this:
[tex]\sin \theta=\frac{h}{a}[/tex]
By replacing 70° for θ and 15 for a, we get:
[tex]\begin{gathered} \sin (70)=\frac{h}{15} \\ \frac{h}{15}=\sin (70) \\ \frac{h}{15}\times15=\sin (70)\times15 \\ h\times\frac{15}{15}=\sin (70)\times15 \\ h\times1=\sin (70)\times15 \\ h=\sin (70)\times15 \\ h=14.1 \end{gathered}[/tex]
Now that we know the length of the side h, we can replace it into the formula of the area:
[tex]A=\frac{14.1\times9}{2}=63.4[/tex]
Then, the area of the triangle equals 63.4 square centimeters
