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somebodys_heartbrake
Find x. the image of an unlabeled triangle with 45 degrees in the upper left corner and a box in the upper right corner; the vertical side on the right of the triangle is labeled 4 and the slanted side from the upper left to the lower right is labeled x A. 4 B. 4 times the square root of 2 C. 8 D. 4 times the square root of 3
by pythagorus theorem: sqrt(4^2 + 4^2) = sqrt(2*(4^2)) = 4*sqrt(2) => answer B
Sides of a 45-45-90 triangle
Find x. image of a triangle whose lower left corner has a box and upper left corner is labeled 30 degrees; the horizontal side of the triangle is labeled 9 and the slanted side from upper left to lower right is labeled x A. 9 B. 18 C. 9 times the square root of 3 D. 3 times the square root of 3
if one is allowed to use trignometry, then 9 = x * sin(30 deg) and so x = 9/sin(30) = 9/(1/2) = 18, which leads to answer B.
Sdes of a 30-60-90 triangle
In a 45°-45°- 90° triangle, if the legs each have a length of 4, then what is the length of the hypotenuse? A. the square root of2 B. 4the square root of2 C. 4 D. 4the square root of3
B. 4*sqrt(2) (reason : pythagorus' theorem). Note that in a 45-45-90 triangle the arms are equal. Proof is by construction where if we lay 2 such triangles side by side, we construct a square (45+45 = 90 degrees)
Find x. image of a triangle whose upper left corner is labeled 60 degrees and upper right corner has a box; the slanted side from upper left to lower right is labeled 16 and the vertical side is labeled x A. 8 B. 8 times the square root of 3 C. 16 times the square root of 3 D. 1 point 8 times the square root of 3