Question

Which equation finds the value of x in the triangle below?

Right triangle X Y Z is shown. Side X Z has a length of 12, side Z Y has a length of x, and hypotenuse X Y has a length of z. The angle opposite to side x is 20 degrees.

Cotangent 70 degrees = StartFraction x Over 12 EndFraction

Cotangent 70 degrees = StartFraction 12 Over x EndFraction

Secant 20 degrees = StartFraction x Over 12 EndFraction

Secant 20 degrees = StartFraction 12 Over x EndFraction

Answer 1

we have that

1) cot 70=x/12

Cot 70=[opposite side]/[adjacent side]=x/12

The option 1 is correct

2) cot 70=12/x

Cot 70=[opposite side]/[adjacent side]=x/12

The option 2 is not correct

3)sec 20=x/12

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 3 is not correct

4) sec 20=12/x

Sec 20 =1/cos20

Cos 20==[opposite side]/[hypotenuse]=12/z

1/(1/cos20)-------> 1/(12/z)------> z/12

The option 4 is not correct

the correct value is

1) cot 70=x/12