If the smaller leg of a 30-60-90 triangle is 4 m, what are the lengths of the longer leg and the hypotenuse?
ratios:
1, sqrt 3, 2
4, 4 sqrt 3, 8
hyp. = 4 / sin30 = 8m.
tan30 = Y/X,
tan30 = 4/X,
X = 4/tan30 = 6.93m.
To find the lengths of the longer leg and hypotenuse of a 30-60-90 triangle, you can use the ratios that exist between the sides. In a 30-60-90 triangle, the ratio of the lengths of the sides is:
Smaller leg : Longer leg : Hypotenuse = 1 : √3 : 2
Given that the smaller leg is 4 m, we can use this ratio to find the lengths of the longer leg and hypotenuse.
Step 1: Multiply the length of the smaller leg by √3 to find the length of the longer leg.
Longer leg = 4 m * √3 ≈ 6.93 m
Step 2: Multiply the length of the smaller leg by 2 to find the length of the hypotenuse.
Hypotenuse = 4 m * 2 = 8 m
Therefore, in this 30-60-90 triangle, the longer leg is approximately 6.93 m and the hypotenuse is 8 m.