The two acute corners of a right triangle are in a ratio of 4: 5. Find a larger sharp corner.

univerkov | September 23, 2021 | education

1. Vertices of the triangle – A, B, C. ∠C = 90 °. ∠А: ∠В = 4: 5.

2. By the condition of the problem ∠А: ∠В = 4: 5. Therefore, ∠А = 4∠В / 5.

3. The total value of all angles of the triangle is 180 °:

∠А + ∠В + ∠С = 180 °. We replace ∠А = 4∠В / 5:

4∠В / 5 + ∠В + 90 ° = 180 °.

9∠B / 5 = 90 °.

∠В = 50 °.

∠А = 4∠В / 5 = 4 x 50 °: 5 = 40 °.

Answer: ∠В = 50 ° – the larger acute angle of the triangle.

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