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3. Hypotenuse 8m, the usual 45/45/90 triangle sides in ratio 1:1:√2.  So we're 8/√2 = 4√2 from the wall.

4√2 meters

4. 30/60/90 right triangle, sides in ratio 1:√3:2.  Hypotenuse 50m, we're after the side opposite 60, so 50/√3 = (50/3) √3

(50/3)√3 meters

5. 45/45/90 again, ratio 1:1:√2.  Leg 3 cm so hypotenuse 3√2

3√2 cm

6. The altitude divides the triangle into two 30/60/90 triangles, ratio 1:√3:2.

The side length s of the original equilateral triangle is the hypotenuse and the altitude h is the long leg, so h= (√3/2) s.

a. 3√3 cm  b. 2√3 cm  c. 5√3 cm

i will pick c put check it over to be sure

step-by-step explanation: