In a right-angled triangle, the leg is 12.8 cm. The length of the height dropped from the top of the right angle

In a right-angled triangle, the leg is 12.8 cm. The length of the height dropped from the top of the right angle to the hypotenuse is 6.4 cm. Find the larger of the angles of the triangle.

1. Vertices of the triangle – А, В, С. А = 90 °. AH = 6.4 centimeters – height (drawn to the hypotenuse BC). AC = 12.8 centimeters.

2. We calculate the value ∠С through the sine of this angle of the ACH triangle:

Sine ∠C = AH: AC = 6.4: 12.8 = 1/2.

An angle whose sine is 1/2 is 30 °. ∠С = 30 °.

3. We calculate the value of the second acute angle (∠В), taking into account that the total value of all angles of the triangle is 180 °:

∠В = 180 – ∠С – А = 180 ° – 30 ° – 90 ° = 60 °.

Answer: a larger acute angle ∠В = 60 °.



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