part of the river she observed fell 1.68 millimeters per year for 1.5 years. Use the distributive property to calculate the exac
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See the attached image for the drawings of the 45-45-90 triangle and the 30-60-90 triangle.
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For the 45-45-90 triangle, the two legs are both 3 while the hypotenuse is unknown. Call it x for now.
Using trig we can say
sin(angle) = opposite/hypotenuse
sin(A) = BC/AC
sin(45) = 3/x
sqrt(2)/2 = 3/x
sqrt(2)*x = 2*3
sqrt(2)*x = 6
x = 6/sqrt(2)
x = (6/sqrt(2))*(sqrt(2)/sqrt(2))
x = (6*sqrt(2)/(sqrt(2)*sqrt(2))
x = (6*sqrt(2)/(2)
x = 3*sqrt(2)
where "sqrt" is shorthand for "square root"
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For the 30-60-90 triangle, we can say
cos(angle) = adjacent/hypotenuse
cos(D) = DE/FD
cos(60) = 4/y
1/2 = 4/y
1*y = 4*2
y = 8
and we can also say
sin(angle) = opposite/hypotenuse
sin(D) = EF/FD
sin(60) = z/y
sin(60) = z/8
8*sin(60) = z
z = 8*sin(60)
z = 8*sqrt(3)/2
z = (8/2)*sqrt(3)
z = 4*sqrt(3)
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For the 45-45-90 triangle, the two legs are both 3 while the hypotenuse is unknown. Call it x for now.
Using trig we can say
sin(angle) = opposite/hypotenuse
sin(A) = BC/AC
sin(45) = 3/x
sqrt(2)/2 = 3/x
sqrt(2)*x = 2*3
sqrt(2)*x = 6
x = 6/sqrt(2)
x = (6/sqrt(2))*(sqrt(2)/sqrt(2))
x = (6*sqrt(2)/(sqrt(2)*sqrt(2))
x = (6*sqrt(2)/(2)
x = 3*sqrt(2)
where "sqrt" is shorthand for "square root"
----------------------------------------------
For the 30-60-90 triangle, we can say
cos(angle) = adjacent/hypotenuse
cos(D) = DE/FD
cos(60) = 4/y
1/2 = 4/y
1*y = 4*2
y = 8
and we can also say
sin(angle) = opposite/hypotenuse
sin(D) = EF/FD
sin(60) = z/y
sin(60) = z/8
8*sin(60) = z
z = 8*sin(60)
z = 8*sqrt(3)/2
z = (8/2)*sqrt(3)
z = 4*sqrt(3)
A<u> triangle</u> is a <em>plane shape</em> bounded by three straight sides, thus it has three internal <em>angles</em>. Therefore, the required <em>values</em> are:
i. x =
ii. y =
A <em>plane shape</em> is a figure bounded by<u> straight</u> sides. Examples are triangles, squares, rectangles, rhombus, kite, trapezium, etc. A triangle is an example of a plane shape that has three<em> sides</em>, thus three <u>angles.</u> also, the sum of <em>angles</em> in a given triangle is .
Thus the required values of x and y can be determined as follows:
x + 20 + 120 =
x + 140 =
x = - 140
So that,
x =
Thus,
y = 20 + 120 (the sum of<em> opposite</em> angles is <em>equal</em> to an exterior angle.)
=
Therefore, x = and y =
For more clafifications on sum of angles in a traingle, visit: brainly.com/question/21680544
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