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Math  /  Trigonometry

QuestionGiven the triangle , find the length of side xx using the Law of Sines. Round your final answer to 4 decimal places. x=x=

Studdy Solution

STEP 1

1. The triangle is non-degenerate and has angles 29∘29^\circ and 21∘21^\circ.
2. The side opposite the 29∘29^\circ angle is 2121 units.
3. The side opposite the 21∘21^\circ angle is xx.

STEP 2

1. Recall the Law of Sines.
2. Set up the equation using the Law of Sines.
3. Solve for xx.
4. Round the answer to 4 decimal places.

STEP 3

Recall the Law of Sines:
asin⁡A=bsin⁡B=csin⁡C \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

STEP 4

Set up the equation using the Law of Sines for the given triangle:
xsin⁡21∘=21sin⁡29∘ \frac{x}{\sin 21^\circ} = \frac{21}{\sin 29^\circ}

STEP 5

Solve for xx:
x=21⋅sin⁡21∘sin⁡29∘ x = \frac{21 \cdot \sin 21^\circ}{\sin 29^\circ}

STEP 6

Calculate the value of xx using a calculator and round to 4 decimal places:
1. Calculate sin⁡21∘\sin 21^\circ.
2. Calculate sin⁡29∘\sin 29^\circ.
3. Compute x=21⋅sin⁡21∘sin⁡29∘x = \frac{21 \cdot \sin 21^\circ}{\sin 29^\circ}.
4. Round the result to 4 decimal places.
x≈21⋅0.35840.4848 x \approx \frac{21 \cdot 0.3584}{0.4848} x≈7.52640.4848 x \approx \frac{7.5264}{0.4848} x≈15.5291 x \approx 15.5291
The length of side xx is approximately:
15.5291 \boxed{15.5291}

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