Question

10. A local park is located on a triangular piece of land. What is the area of the park to the nearest tenth? (1 point) S 75 m 40° R 150 m T Area = m2​

Answer 1

Area equals to 3615.7

Explanation:

So first in order to get the area of the triangle you need to have it’s height and base. We know the base is 150m(you can choose another base too), and we need to get the height.

In order to get the height we can see the triangle as two right triangle spreaded by the height. Now looking at the right triangle at the left hand, realized this triangle has a 40, a 90 degree angle and a side of 75.

Next using the law of sines, and plot the numbers in:

a = b(sinα/sinβ)=75(sin(40°)/sin(90°))≈48.20907

Now calculat the area;

Area = 1/2 bh = 1/2 (150x48.20907) ≈ 3615.6765

I attached a graph below that may help to see will all the things go