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.

Answer 1

cot(70)=x/12

Explanation:

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Answer 2

B. cot70 = 12/x

Explanation:

The question lacks appropriate option Find the options below;

Answers to choose from are:

a) cot70 = x/12

b) cot 70= 12/x

c) sec 20= x/12

d) sec20 = 12/x

Given the triangle as shown in the attachment, to get the value of x, we will use one of the trigonometry ratio SOH, CAH, TOA

given ZY = x = opposite

XY = z = hypotenuse

XZ = 12 = adjacent

∠X = 20°

∠Z = 90°

Since sum of angle in the triangle is 180°, ∠X+∠Y+∠Z = 180°

20+∠Y + 90 = 180

∠Y = 180-110

∠Y = 70°

According to TOA,

tan∠X = opp/adj = ZY/XZ

tan70= x/12

since cot70 = 1/tan70

reciprocating both sides will give;

1/tan70 = 12/x

cot70 = 12/x

This gives the required expression