Write the ratios for sin x, cos x and tan x
1 answer:
Answer:
sin(x)= / 12, cos(x)=5/12, tan=
/ 5
Step-by-step explanation:
segment YZ is length a, we need to find a
segment XZ is length 5
segment XY is length 12
XYZ is a right triangle, so a^2 + b^2 = z^2, so
a^2 + 5^2 = 12^2, simplify
a^2 + 25 = 144, subtract 25
a^2 = 119
a =
then we can determine all the trig ratios
soh - cah - toa
sin = opp/hyp, cos=adj/hyp, tan=opp/adj
sin(x)= / 12, cos(x)=5/12, tan=
/ 5
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A diagram of parallelogram MNOP is attached below
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>