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In /_\JKL,j=4.1cm,l=1.2cm and /_L=29^(@). Find all possible values of /_J, to the nearest 1oth of a degree. Answer:

In △JKL,j=4.1 cm,l=1.2 cm \triangle \mathrm{JKL}, j=4.1 \mathrm{~cm}, l=1.2 \mathrm{~cm} and ∠L=29∘ \angle \mathrm{L}=29^{\circ} . Find all possible values of ∠J \angle \mathrm{J} , to the nearest 1010th of a degree.\newlineAnswer:

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Q. In △JKL,j=4.1 cm,l=1.2 cm \triangle \mathrm{JKL}, j=4.1 \mathrm{~cm}, l=1.2 \mathrm{~cm} and ∠L=29∘ \angle \mathrm{L}=29^{\circ} . Find all possible values of ∠J \angle \mathrm{J} , to the nearest 1010th of a degree.\newlineAnswer:
  1. Apply Law of Sines: To find the possible values of ∠J\angle J, we can use the Law of Sines, which relates the lengths of sides of a triangle to the sines of its opposite angles. The Law of Sines states that for any triangle ABCABC with sides aa, bb, and cc opposite angles AA, BB, and CC respectively, the following ratio holds true: (sin⁡A)/a=(sin⁡B)/b=(sin⁡C)/c(\sin A)/a = (\sin B)/b = (\sin C)/c. We will apply this to triangle JKLJKL.
  2. Find length of side kk: First, we need to find the length of side kk opposite angle /L/_L. We can use the Law of Sines to find this. We have two sides and one angle, so we can write the equation as sin⁡Ll=sin⁡Jj\frac{\sin L}{l} = \frac{\sin J}{j}. We know LL and ll, so we can solve for sin⁡J\sin J.sin⁡29∘1.2=sin⁡J4.1\frac{\sin 29^\circ}{1.2} = \frac{\sin J}{4.1}
  3. Calculate sin⁡29∘\sin 29^\circ: Now we calculate sin⁡29∘\sin 29^\circ using a calculator.sin⁡29∘≈0.4848\sin 29^\circ \approx 0.4848
  4. Substitute sin⁡29∘\sin 29^\circ: Substitute the value of sin⁡29∘\sin 29^\circ into the equation and solve for sin⁡J\sin J.0.48481.2=sin⁡J4.1\frac{0.4848}{1.2} = \frac{\sin J}{4.1}sin⁡J≈0.4848×4.11.2\sin J \approx \frac{0.4848 \times 4.1}{1.2}
  5. Perform multiplication and division: Perform the multiplication and division to find sin⁡J\sin J.sin⁡J≈1.987281.2\sin J \approx \frac{1.98728}{1.2}sin⁡J≈1.6561\sin J \approx 1.6561

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