Method 1: Equilateral triangles (also are equiangular - each angle 60 degrees) have all sides the same length... and an altitude from a vertex will bisect (cut in half) the side it intersects. Also, a 2 congruent right triangles are formed.
9. 4 ft = side length (this will be the hypotenuse when the altitude drops)
2 ft = one of the legs in the new right triangle
[tex] a^{2} + b^{2} = c^{2} [/tex]
a² + 2² = 4²
a² + 4 = 16
a² = 12
a = [tex] \sqrt{12} = \sqrt{4} [/tex]×[tex] \sqrt{3} =2 \sqrt{3} [/tex]ft
Method 2: Using the information about 30 - 60 - 90 right triangle
The side opposite the 30 degree angle is half of the hypotenuse and the side opposite the 60 degree angle is the side opposite the 30 angle × [tex] \sqrt{3} [/tex]. The altitude is the side opposite the 60 degree angle...
10. altitude = [tex] \frac{1}{2} [/tex](given side length of equilateral triangle)[tex] \sqrt{3} [/tex]
altitude = [tex] \frac{1}{2} (27.4) \sqrt{3} =13.7 \sqrt{3} [/tex]m
11. altitude = [tex] \frac{1}{2} ( \frac{2}{3} ) \sqrt{3}= \frac{1}{3} \sqrt{3} [/tex]=[tex] \frac{ \sqrt{3} }{3} [/tex]yd
12. If the perimeter is 24 units then a side is 24 units/3 = 8 units.
altitude = [tex] \frac{1}{2}(8) \sqrt{3} =4 \sqrt{3} [/tex] units
