Question

Help me with geometry please :(

Answer 1

Angle LKM is the same as angle K

angle LMK is the same as angle M

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Part (a)

sin(angle) = opposite/hypotenuse

sin(K) = ML/MK

sin(K) = 12/13

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Part (b)

cos(angle) = adjacent/hypotenuse

cos(K) = KL/MK

cos(K) = 5/13

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Part (c)

tan(angle) = opposite/adjacent

tan(K) = ML/LK

tan(K) = 12/5

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Part (d)

sin(angle) = opposite/hypotenuse

sin(M) = LK/MK

sin(M) = 5/13

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Part (e)

cos(angle) = adjacent/hypotenuse

cos(M) = ML/MK

cos(M) = 12/13

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Part (f)

tan(angle) = opposite/adjacent

tan(M) = KL/ML

tan(M) = 5/12

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Part (g)

From part (a), we found that sin(K) = 12/13, so,

sin(K) = 12/13

arcsin(sin(K)) = arcsin(12/13)

K = arcsin(12/13)

K = 67.380135

Angle LKM is approximately 67.380135 degrees

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Part (h)

Angle K and angle M are complementary. They add to 90 degrees

K+M = 90

67.380135+M = 90

67.380135+M-67.380135 = 90-67.380135

M = 22.619865

Angle LMK is roughly 22.619865 degrees