Question

What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to help find the height. Show work.

Answer 1

Answer: 55.4

Step-by-step explanation:

The right triangle shown here is a 30-60-90 triangle. This means that its angles measure 30, 60, and 90 degrees. (I got the 30 degrees by subtracting the other two angles from 180 degrees, as the sum of the angle measures in a triangle is 180 degrees.)

The sides in such a triangle have the ratio of x:x$\sqrt{3}$:2x

The x is across from the 30 degree angle, the x$\sqrt{3}$ is across from the 60 degree angle, and the 2x is across from the 90 degree angle.

The x in this triangle equals to 8 as the eight is across from the 30 degree angle.

This means that the x$\sqrt{3}$ side will equal 8$\sqrt{3}$.

That side is also the height of the triangle. The area of the triangle is then 1/2(8)(8$\sqrt{3}$), or about 55.4.