In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit. C = 102°, a = 16 meters, b = 20 meters

검증된 단계별 안내

Identify the given elements of the triangle: angle \(C = 102^\circ\), side \(a = 16\) meters, and side \(b = 20\) meters. We need to find the area of the triangle.

Recall the formula for the area of a triangle when two sides and the included angle are known: \(\text{Area} = \frac{1}{2}ab \sin C\).

Substitute the known values into the formula: \(\text{Area} = \frac{1}{2} \times 16 \times 20 \times \sin 102^\circ\).

Calculate \(\sin 102^\circ\) using a calculator or trigonometric tables to find the sine of the given angle.

Multiply the values together to find the area, then round the result to the nearest whole number as requested.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Law of Cosines

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is useful for finding an unknown side or angle when two sides and the included angle are known, or vice versa. In this problem, it helps confirm the triangle's dimensions or find missing elements if needed.

Area of a Triangle Using Two Sides and Included Angle

The area of a triangle can be calculated using the formula (1/2)ab sin(C), where a and b are two sides and C is the included angle. This formula is especially useful when the height is unknown but two sides and the included angle are given, as in this problem.

Trigonometric Functions and Angle Measurement

Understanding how to use trigonometric functions like sine and cosine with angles measured in degrees is essential. Correctly applying sin(102°) ensures accurate calculation of the area. Familiarity with converting and using angles in degrees is important for precise results.