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 your work). Will Only Mark Brainliest if answered correctly and No resharing another students answer from brainly or any other websites or you'll be reported. ​

Answer 1

Answer:

Area = 21.7 cm² (nearest tenth)

Step-by-step explanation:

A 30-60-90 triangle is a special right triangle.  The measures of its sides have a special relationship in that they are in proportion:

shortest leg : longest leg : hypotenuse =  1 : √3 : 2

• The side opposite 30° is the shortest leg
• The side opposite 60° is the longest leg and is √3 times the length of the shorter leg.
• The side opposite 90° is the hypotenuse and is twice the length of the shorter leg.

So we can also write the ratio as  $x : x\sqrt{3} : 2x$  where $x$ is the shortest side.

From inspection of the diagram, the shortest side is 5 cm

⇒ BC (height) = 5 × √3 = 5√3 cm

Now we have the height, we can calculate the area.

Area of a triangle = 1/2 x base x height

                             = 1/2 x 5 x 5√3

                             = 21.7 cm² (nearest tenth)