# In a rectangular triangle, the leg adjacent to the 60 degree angle is 13 cm. Enter the second acute angle

September 28, 2021 | education

| Since this triangle is right-angled, and the sum of all the angles of the triangle is 180 °, the second acute angle will be equal to:

180 – 60 – 90 = 180 – 150 = 30 °.

As you know from the property of a right-angled triangle, the leg, which lies opposite an angle of 30 °, is equal to 1/2 of the hypotenuse of the triangle, so the length of the hypotenuse will be equal to:

2 * 13 = 26 cm.

We find the length of the second leg according to the Pythagorean theorem.

a ^ 2 = 26 ^ 2 – 13 ^ 2 = 676 – 169 = 507.

√а = √507 = 22.5 cm.

Answer:

The length of the hypotenuse is 26 cm, the acute angle is 30 °.

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