All the sides of an equilateral triangle are the same, and all three angles are 60 degrees. If we want the height of the triangle, we can draw a vertical line straight down the center. This will bisect the top angle into two 30 degree angles and form a 90 degree corner at the base. The base will be split into two equal pieces. In this case 14 and 14 (half of 28).
To find the height, we can use a couple methods. First is Pythagorean Theorem which states that a^2 + b^2 = c^2. We know c = 28 and a = 14, so we can solve for the height. b = sqrt(28^2 - 14^2) = sqrt(588).. 588 can be factored into 196 and 3. So we can simplify the radical to 14sqrt(3).
The second way to find the height is to use trigonometry. We can use cos(30) = h/28 and solve for h to get h = 28cos30 or 14sqrt(3).
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The next problem is asking the same thing. The altitude is the height. So use either of the methods above to get 2sqrt(3).
(On the far left, it says 140 at the top and then 5 to the left of 28) The answer is 35, let me know if you can't read anything or have any questions. Hope this helped :)
