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Determine the value of the unknown triangles, correct to 1 decimal place. 2. Determine the area of triangle ABC (correct to one decimal place).

Mathematics

ScanSolve AI Answer

Answer

398.8

Step-by-step solution

3 steps

To determine the area of triangle ABC, we use the values calculated previously:
∠A=33∘\angle A = 33^\circ
∠B=82∘\angle B = 82^\circ
∠C=65∘\angle C = 65^\circ
Side a=22a = 22
Side b≈40.0b \approx 40.0
Side c≈36.6c \approx 36.6

  1. Identify the formula for the area of a triangle.

    The area of a triangle can be calculated using the formula involving two sides and the included angle:

    Area=12acsin⁡B\text{Area} = \frac{1}{2}ac \sin B
  2. Substitute the known values into the formula.

    Using a=22a = 22, c≈36.610c \approx 36.610 (from previous calculation before rounding), and ∠B=82∘\angle B = 82^\circ:

    Area=12×22×36.610×sin⁡82∘\text{Area} = \frac{1}{2} \times 22 \times 36.610 \times \sin 82^\circ
  3. Calculate the area and round to one decimal place.

    Area=11×36.610×sin⁡82∘\text{Area} = 11 \times 36.610 \times \sin 82^\circ Area≈11×36.610×0.990268\text{Area} \approx 11 \times 36.610 \times 0.990268 Area≈398.800\text{Area} \approx 398.800

    Rounding to one decimal place:

    Area≈398.8\text{Area} \approx \boxed{398.8}
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