Answer:
- Jedi light saber: 6 ft
- Darth light saber: 5 ft
Step-by-step explanation:
Given
Find
The length of each light saber, rounded up to the nearest foot.
Solution
The attached scale drawing shows the triangles with the angles and sides filled in.
The angle at the Jedi's hand is 2a = 2(37°) = 74°. If L represents the Jedi's light saber length, then the cosine relation is useful:
Cos = Adjacent/Hypotenuse
cos(74°) = (1.4 ft)/L
L = (1.4 ft)/cos(74°) ≈ 5.08 ft
Rounded up to the nearest foot, the Jedi's light saber is 6 ft long.
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The angle at Darth's hand is ...
5c = 5(16°) = 80°
and the length of the opposite side is ...
b/14 = 63/14 = 4.5 . . . feet
The sine relation is useful here. If L represents Darth's light saber length, then ...
Sin = Opposite/Hypotenuse
sin(80°) = (4.5 ft)/L
L = (4.5 ft)/sin(80°) ≈ 4.57 ft
Rounded up to the nearest foot, Darth's light saber is 5 ft long.
