The outer angle at the vertex A of the right-angled triangle ABC is 150 °. AB + BC = 27 cm. Find BC if angle C is straight.
| January 28, 2021 | education
The ВAD angle and the BAC angle are adjacent angles, the sum of which is 1800. Then the BAC angle = 180 – ВAD = 180 – 150 = 300.
By condition, AB + BC = 27 cm. (1).
In a right-angled triangle ABC, the leg BC is located opposite an angle of 300, then:
BC = AB / 2. (2).
Let us solve the system of equations 1 and 2 by the substitution method.
AB = 27 – BC.
BC = (27 – BC) / 2.
2 * BC + BC = 27.
3 * BC = 27.
BC = 27/3 = 9 cm.
AB = 27 – 9 = 18 cm.
Answer: The length of the BC side is 27 cm.
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