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.
Answer: 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
Answer: (50/3)√3 meters
5. 45/45/90 again, ratio 1:1:√2. Leg 3 cm so hypotenuse 3√2
Answer: 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.
Answer: a. 3√3 cm b. 2√3 cm c. 5√3 cm