Question

Triangle JKL, Which expression can be used to find the value of X ? Angle L equals 32 angle K= 47° side JL equals 11 side JK=X

Answer 1

In a triangle, the sum of the interior angles is always equal to 180 degrees. Therefore, we can use the following formula to find the measure of angle J:

Angle J = 180 - Angle K - Angle L

Substituting the given values, we get:

Angle J = 180 - 47 - 32 = 101 degrees

Now that we know the measure of angle J, we can use the Law of Cosines to find the length of side JK:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the side opposite to angle C, and a and b are the other two sides of the triangle. Substituting the given values, we get:

X^2 = 11^2 + X^2 - 2(11)(X)*cos(101)

Simplifying:

X^2 = 121 + X^2 - 22X*cos(101)

22X*cos(101) = 121

X = 121 / (22*cos(101))

X ≈ 4.31

Therefore, the expression that can be used to find the value of X is X ≈ 4.31.