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 your work!!!

We have been given an image of a 30-60-90 triangle. We are asked to find the area of our given triangle.First of all, we need to find the height of our given triangle.In a 30-60-90 triangle, the shorter leg that corresponds to 30 degree angle is units long. The sides corresponding to 60 and 90 degree angles are and respectively.Since the value of is 5 cm, so the height of our given triangle (corresponding to 60 degree angle) will be:Upon substituting our given values in area of triangle formula we will get,Therefore, the area of our given triangle is 21.7 square centimeters.

kesme981 kesme981 · Answer 2 · 2020-05-08T04:21:05+02:00

Answer:

[tex]31.2[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

To find the area, you first need the measure of the other leg, AB. We know two angles, one of 90° and the other of 60°. Since a triangles angles will always add up to a total of 180°, we can conclude that the other angle is 30°. You can use the 30°-60°-90° theorem:

[tex]longer[/tex] [tex]leg=\sqrt{3}*shorter[/tex] [tex]leg[/tex]

Insert the values. Let [tex]l[/tex] be AB:

[tex]l=\sqrt{3}*6[/tex]

Simplify:

[tex]l=6\sqrt{3}[/tex]

The length of AB is [tex]6\sqrt{3}[/tex].

Use this to find the area:

[tex]A=\frac{ab}{2}[/tex]

a and b are the legs, as in the Pythagorean theorem. Insert the values:

[tex]A=\frac{6*6\sqrt{3} }{2}[/tex]

Simplify multiplication:

[tex]A=\frac{36\sqrt{3}}{2}[/tex]

Simplify division:

[tex]A=18\sqrt{3}[/tex]

Convert to decimal:

[tex]A=31.18[/tex]

Round to the nearest tenth:

[tex]A=31.2[/tex]

The triangle has an area of [tex]31.2[/tex] [tex]cm^2[/tex].

Finito.