Simplify the following expression, giving the answer in index notation: 8^12/8^2. Question (j)
1 answer:
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Answer and Step-by-step explanation:
You are correct in that we need to use the Law of Sines: .
Here, when we use the Law of Sines, we have: .
Cross multiply:
(sinB) * 28 = (sin63) * 29
28sinB ≈ 25.839
sinB ≈ 0.9228
Now, in order to solve for B, we need to use inverse sin ():
The sines on the left cancel out, and we're left with:
B ≈ 67.3 degrees
Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:
180 - 67.3 = 112.7 degrees.
Hope this helps!
Answer:
Length:8 m
Width:3 m
Step-by-step explanation:
<u><em>The complete question is</em></u>
If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.
step 1
<em>Perimeter of rectangle</em>
we know that
The perimeter of rectangle is equal to
we have
so
Simplify
-----> equation A
step 2
Perimeter of triangle
The perimeter of triangle is equal to
so
Multiply by 2 both sides
----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (8,3)
see the attached figure
therefore
The dimensions of the rectangle are
Length:8 m
Width:3 m
