Answer:
(a) α = 60°, β = 30°
(b) α ≈ 67.4°, β ≈ 22.6°
Step-by-step explanation:
I'll do (a) and (b) as examples. Make sure your calculator is set to degrees, not radians.
(a) For α, we're given the opposite and adjacent sides, so use tangent.
tangent = opposite / adjacent
tan α = √300 / 10
tan α = √3
α = 60°
Since angles of a triangle add up to 180°, we know that β = 30°. But we can use tangent again to prove it:
tan β = 10 / √300
tan β = 1 / √3
tan β = √3 / 3
β = 30°
(b) For α, we're given the adjacent side and the hypotenuse. So use cosine.
cos α = adjacent / hypotenuse
cos α = 15 / 39
cos α = 5 / 13
α ≈ 67.4°
Again, we know that β = 22.6°, but let's show it using trig. We're given the opposite side and hypotenuse, so use sine:
sin β = 15 / 39
sin β = 5 / 13
β ≈ 22.6°
Answer:
Step-by-step explanation:
The volume of the prism is 3 cube units, which means that the prism can be filled with 3 
.
Here, there are 64 cubes with 1/4 units side lengths in 1 cubic unit.
Since the rectangular prism is made up of 3 cubic units, we would have
3 * 64 total cubes with 1/4 units side lengths.
Therefore, it takes 192 of the 1/4 unit cubes to fill the prism.
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Answer:
Step-by-step explanation:
13 - 17 = 4
Answer is 5/29. Because 3/29 + 2/29=5/29
1 cup equals 8 ounces. 4×8=32. So, Jimay has 32 ounces of sugar.
