Answer: Choice B
- JK = 3.51
- WK = 9.15
- angle J = 69 degrees
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Step-by-step explanation:
Angle W = 21 degrees is the reference angle.
Opposite this reference angle is side JK.
The hypotenuse is WJ = 9.8
Use the sine ratio to connect the opposite and hypotenuse.
sin(angle) = opposite/hypotenuse
sin(W) = JK/WJ
sin(21) = JK/9.8
JK = 9.8*sin(21)
JK = 3.51200590554394 approximately
JK = 3.51 approximately
Make sure your calculator is in degree mode.
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We can use the cosine ratio to determine side WK
cos(angle) = adjacent/hypotenuse
cos(W) = WK/WJ
cos(21) = WK/9.8
WK = 9.8*cos(21)
WK = 9.14908817967258 approximately
WK = 9.15 approximately
Or alternatively you can use the tangent ratio and solve for WK in the equation below
tan(21) = JK/WK
Yet another alternative is to use the pythagorean theorem
a^2+b^2 = c^2
With a = 3.51, b = unknown, and c = 9.8
You should get b = 9.15 after applying the pythagorean theorem. Once you know two sides of a right triangle, a bunch of options open up.
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Angle J is found by subtracting the value of angle W from 90
W+J = 90
J = 90 - W
J = 90 - 21
J = 69 degrees
Or you could say
W+K+J = 180
21+90+J = 180
111+J = 180
J = 180-111
J = 69 degrees
But I prefer the first set of steps as it's faster.
You could use inverse trig functions to determine angle J, but it will require a calculator and it may not be as intuitive.