The side of a rhombus is 15 centimeters long, and the length of its longer diagonal is 24.6 centimeters. Find the area.
1 answer:
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9514 1404 393
Answer:
D
Step-by-step explanation:
In the second quadrant, ...
c = 180° -arcsin(24/25) ≈ 106.26°
In the third quadrant, ...
d = 360° -arccos(-3/4) ≈ 221.41°
Then cos(c+d) = cos(327.67°) ≈ 0.84498
This is a positive irrational number, greater than 21/100, so the only reasonable choice is the last one:
_____
Perhaps you want to work this out using the trig identities.
cos(c) = -√(1 -sin(c)²) = -7/25
sin(d) = -√(1 -cos(d)²) = -(√7)/4
Then the desired cosine is ...
cos(c+d) = cos(c)cos(d) -sin(c)sin(d)
cos(c+d) = (-7/25)(-3/4) -(24/25)(-√7/4)
cos(c+d) = (21 +24√7)/100 . . . . matches choice D
Pemdas? OK so how I would remember it by is "Please Excuse My Dear Aunt Sally"
So.. Parenthesis, Exponent(s), Multiplication, Division, Addition, Subtraction..
Example~~~~~
(
+ 4) ×12÷4 - 1= ? so first do parenthesis and then the exponents then add it to 4 and the divide 12 and 4 and then subtract 1 which is 2.. Then after take two and 13 and multiply which is 26~
Hope this helps! :)
So.. Parenthesis, Exponent(s), Multiplication, Division, Addition, Subtraction..
Example~~~~~
(
Hope this helps! :)