Answer:
- sin C=h/a
- substitution property of equality
- commutative property of multiplication
Step-by-step explanation:
Because two points determine a line, you can draw altitude BD perpendicular to AC with height h. By the definition of a sine ratio, <u>sin(C) = h/a</u>, which can be rearranged into a·sin(C) = h. The area of △ABC is A=1/2bh. The <u>substitution property of equality</u> can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the <u>commutative property of multiplication</u>.
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The mnemonic SOH CAH TOA reminds you that the sine ratio is ...
Sin = Opposite/Hypotenuse
Here, the side of the right triangle opposite angle C is designated "h", the height of ∆ABC. The hypotenuse of that right triangle is side "a". So ...
sin(C) = h/a
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The substitution property of equality lets you replace any expression with its equal. Here, we have h=a·sin(C), so we can use a·sin(C) in place of h in the formula for triangle area:
1/2bh = 1/2ba·sin(C)
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The commutative property of multiplication lets you rearrange the order of the factors in a product, so ...
ba = ab
and
A = 1/2ba·sin(C) = 1/2ab·sin(C)
I believe the answer is
.5
Answer:
c=71/23 or 3 2/23 or 3.08695652...
Width of the rectangle is 14 ft
Step-by-step explanation:
- Step 1: Let the width of the rectangle be x. Then length = 8 + x. Perimeter = 72 ft.
Perimeter = 2(length + width)
72 = 2 (8 + x + x)
72 = 16 + 4x
4x = 56
x = 56/4 = 14
∴ Width of the rectangle is 14 ft
Answer:
A, C,D,E,F
Step-by-step explanation:
