Question

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

Answer 1

by pythagorus theorem: sqrt(4^2 + 4^2) = sqrt(2*(4^2)) = 4*sqrt(2) => answer B

Answer 2

Sides of a 45-45-90 triangle

Answer 3

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

Answer 4

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.

Answer 5

Sdes of a 30-60-90 triangle

Answer 6

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

Answer 7

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)

Answer 8

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