Answer:
c = (7/2)√3
a = (3/2)√2
Step-by-step explanation:
You want the length of the adjacent side in the special right triangles shown.
Cosine
The unknown side in each triangle is the side adjacent to the angle. The known side is the hypotenuse. This tells us we can make use of the relation ...
Cos = Adjacent/Hypotenuse
Adjacent = Hypotenuse × Cos
The ratios of side lengths in these triangles are ...
30°-60°-90° triangle: 1 : √3 : 2 ⇒ cos(30°) = (√3)/2
45°-45°-90° triangle: 1 : 1 : √2 ⇒ cos(45°) = 1/√2 = (√2)/2
Application
c = 7 · cos(30°)
c = (7/2)√3
a = 3 · cos(45°)
a = (3/2)√2
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