SOLUTION: Triangle ABC has these measurements angle A = 90 degrees angle B = 34 degrees measurement of b = 14 cm 1) Sketch the triangle ABC 2) Which of the 2 legs do you think is lon

Question 694557: Triangle ABC has these measurements
angle A = 90 degrees
angle B = 34 degrees
measurement of b = 14 cm
1) Sketch the triangle ABC
2) Which of the 2 legs do you think is longer. Explain your answer
3) Determine the lengths of a and c than verify you answer in part 2.

can you please help me I really don't get ? Thanks in advance :)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Triangle ABC has these measurements
angle A = 90 degrees
angle B = 34 degrees
measurement of b = 14 cm
1) Sketch the triangle ABC
You have a right triangle with:
hypotenuse opposite angle A
side b = 14 cm is opposite angle B which equals 34 degrees
--------------------------------------------------------------
2) Which of the 2 legs do you think is longer. Explain your answer
Angle C = 90-34 = 56 degrees.
Since Angle C > Angle B, leg c > legb which is 14 cm
-------------------------------
3) Determine the lengths of a and c than verify your answer in part 2.
Use the Law of Sines:
c/sin(C) = b/sin(B)
c = sin(56 deg)[14/sin(34)] = 20.76 cm
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Cheers,
Stan H.
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