# In a right-angled triangle, angle C is a straight line, angle A is 60 degrees. The sum of the sides AC and AB

March 30, 2021 | education

| **In a right-angled triangle, angle C is a straight line, angle A is 60 degrees. The sum of the sides AC and AB is 51 cm. What are angle B, leg AC and hypotenuse AB?**

1. We calculate the degree measure of the angle ∠В:

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

2. The AC leg is opposite the 30 ° angle. Therefore, according to one of the properties of a rectangular

triangle, its length is equal to 1/2 the length of the hypotenuse AB. Therefore, AB = 2 AC.

3. By the condition of the problem, AS + AB = 51 cm.

4. Replace AB in this expression with 2 AC:

АС + 2АС = 51 cm.

AC = 17 cm.

AB = 17 x 2 = 34 cm.

Answer: ∠В = 30 °, the length of the AC leg is 17 cm, the length of the hypotenuse AB is 34 cm.

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