Answer:
7. one triangle
8. two triangles
Step-by-step explanation:
When you are given two sides and one of the opposite angles, you can make a determination as follows:
- If the given angle is <em>opposite the longest given side</em>, there is one solution.
- If the given angle is <em>opposite the shortest given side</em>, there may be 0, 1, or 2 solutions.
For the latter case, the possibilities for sides b, c, and angle C are ...
C > 90° . . . . . . . . no solution
(b/c)sin(C) > 1 . . . no solution
(b/c)sin(C) = 1 . . . 1 solution
(b/c)sin(C) < 1 . . . 2 solutions
(The expression (b/c)sin(C) gives sin(B), so the value must lie within the range of the sine function in order for there to be any solution.)
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7. The given angle is opposite the <em>longest</em> given side. There is one solution.
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8. The given angle is opposite the <em>shortest</em> given side, so we compute
(b/c)sin(C) = (34/28)sin(20°) ≈ 0.41
This is less than 1, so there are two solutions.
The formula of an area of a rhombus:
The diagonals bisect each other. That is, they divide each other into two equal parts.
Therefore we have:
Substitute:
Answer: 2.16 m²
Use elimination to create a one variable equation.
x-3y=15 -> 2x-6y=30
2x-6y=30
+(-2x-4y=10)
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-10y=40
Then solve (for y in this case).
y=-4
Now we can use the value for y to solve for x.
x-3y=15 -> x-3(-4)=15 -> x=3
Perimeter (P) = 2L + 2w
64 = 2L + 2w
64 - 2L = 2w
32 - L = w
Area (A) = L x w
= L x (32 - L)
= 32L - L²
To find maximum area, calculate the derivative and set it equal to zero.
A' = 32 - 2L
0 = 32 - 2L
2L = 32
L = 16
Substitute L to solve for y: 32 - L = w → 32 - 16 = w → 16 = w
The maximum area will be 16 ft x 16 ft = 256 ft²