In a trapezium ABCD with AB || DC, AB = 17 cm, AD = 16 cm, and angle ABC = 150 degrees. Given AB = BD = 17 cm, find the length of BC.

April 24, 2026Mathematics

ScanSolve AI Answer

April 24, 2026

Answer

17 $cm,$ AD = 16 $cm,$ \angle ABC = 150^\circ$.

Here's the solution to the problem:

a) The length of BC Step 1: Identify known values and properties. We are given $AB = 17$ cm, $AD = 16$ cm, $\angle ABC = 150^\circ$ . We are also given that $AB = BD = 17$ cm. This means $\triangle ABD$ is an isosceles triangle. Since $AB \parallel DC$ , $ABCD$ is a trapezium.

Step 2: Calculate $\angle ABD$ using the Cosine Rule in $\triangle ABD$ . In $\triangle ABD$ , sides are $AB=17$ , $BD=17$ , $AD=16$ .

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Here's the solution to the problem: a) The length of BC Step 1: Identify known values and properties.

Asked on April 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 24, 2026

Here's the solution to the problem: a) The length of BC Step 1: Identify known values and properties. We are given AB = 17 cm, AD = 16 cm, ABC = 150^. We are also given that AB = BD = 17 cm. This means ABD is an isosceles triangle. Since AB DC, ABCD is a trapezium. Step 2: Calculate ABD using the Cosine Rule in ABD. In ABD, sides are AB=17, BD=17, AD=16. AD^2 = AB^2