Question

a right triangle has one angle that measure 23°. the adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. what is the approximate area of the triangle? round to the nearest tenth. area of a triangle = \\(\frac{1}{2}bh\\) \\(\bigcirc\\) 68.7 cm² \\(\bigcirc\\) 161.8 cm² \\(\bigcirc\\) 381.3 cm² \\(\bigcirc\\) 450.0 cm²

Explanation:

Step1: Find opposite leg length

Use sine: $\sin(23^\circ) = \frac{\text{opposite}}{30}$
$\text{opposite} = 30 \times \sin(23^\circ) \approx 30 \times 0.3907 = 11.721$ cm

Step2: Identify base and height

Base = adjacent leg = 27.6 cm, height = opposite leg ≈ 11.721 cm

Step3: Calculate triangle area

Use formula: $\text{Area} = \frac{1}{2} \times b \times h$
$\text{Area} = \frac{1}{2} \times 27.6 \times 11.721 \approx 13.8 \times 11.721 \approx 161.75$ cm²

Step4: Round to nearest tenth

$161.75 \approx 161.8$ cm²

Answer:

161.8 cm²