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 where
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)
