Question

a right triangle has one angle that measures 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\\) 68.7 cm² 161.8 cm² 381.3 cm² 450.0 cm²

Explanation:

Step1: Identify needed leg

Opposite leg via sin(23°): $opposite = hypotenuse \times \sin(23^\circ)$

Step2: Calculate opposite leg

$opposite = 30 \times \sin(23^\circ) \approx 30 \times 0.3907 \approx 11.72$ cm

Step3: Compute area

$Area = \frac{1}{2} \times adjacent \times opposite = \frac{1}{2} \times 27.6 \times 11.72 \approx 161.8$ cm²

Answer:

B. 161.8 cm²