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what is the trigonometric ratio for sin z ?
enter your answer, as a simplified fraction, in the blanks.

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Need some what is the trigonometric ratio for sin z ?  enter your answer, as a simplif

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Sorry this is a late response, I have just got done taking it myself. The answer is 3/5. You have 40 and 32, so you try figuring out (since you're simplifying) the LOWEST common multiple in this case. Since you always put the smallest number (the ones given to you which in this case is 32) as the numerator, the largest [is 40] making it the denominator. Apparently, the answer is 3/5. I argue that because there is no number between these two that three goes into, since the smallest that goes into 32 is 4. If they'd fix the answer, it'd be 4/5. Other than that, put down 3/5.
Side AC4/33/57/254 meters
Problem 1

side AC



Explanation:

Side AC is opposite angle B because it is the furthest you can get on the triangle to be away from point B. This segment is a leg of the right triangle. Note how the letter B is not anywhere to be found in AC.


Problem 2

4/3



Explanation:

angle D is the right angle, the side across from this right angle is the hypotenuse EF

with reference angle F, we have
opposite = ED = 4
adjacent = DF = 3

tan(angle) = opposite/adjacent
tan(F) = ED/DF
tan(F) = 4/3


Problem 3

3/5



Explanation:

Use the Pythagorean Theorem to find the missing side XY
a^2 + b^2 = c^2
(XY)^2 + (YZ)^2 = (XZ)^2
(XY)^2 + (32)^2 = (40)^2
(XY)^2 + 1024 = 1600
(XY)^2 + 1024-1024 = 1600-1024
(XY)^2 = 576
sqrt[ (XY)^2 ] = sqrt[ 576 ]
XY = 24

Use that value to find the trig ratio we need

sin(angle) = (opposite)/(hypotenuse)
sin(Z) = (XY)/(XZ)
sin(Z) = (24)/(40)
sin(Z) = (8*3)/(8*5)
sin(Z) = 3/5


Problem 4

7/25



Explanation:

cos(angle) = adjacent/hypotenuse
cos(D) = (ED)/(DF)
cos(D) = (21)/(75)
cos(D) = (7*3)/(25*3)
cos(D) = 7/25


Problem 5

4 meters



Explanation:

We want to find the horizontal distance from the ground to the foot of the ladder. Call this x for now. 

This x is the adjacent leg, since it is touching the 63 degree angle. The opposite side is 8 meters

opposite = 8
adjacent = x

Use the tangent function to solve for x

tan(angle) = opposite/adjacent
tan(63) = 8/x
x*tan(63) = x*(8/x)
x*tan(63) = 8
x*tan(63)/tan(63) = 8/tan(63)
x = 4.07620359595543
Rounding to the nearest whole number, we get 4 meters.

In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.

So, in your case, we have

\sin(Z) = \dfrac{XY}{XZ}

In order to find XY, we have

XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24

So, the ratio for the sine is

\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}

Cos Z = 32/40 => Z= cos-¹(32/40) =>

sin Z = sin (cos-¹(32/40)) = 3/5
Cos Z = 32/40 => Z= cos-¹(32/40) =>

sin Z = sin (cos-¹(32/40)) = 3/5


Do you know the answer?

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