In a right-angled triangle ABC, the hypotenuse AB is 12 centimeters and the angle A is 60 ‘CD

| January 29, 2021 | education

In a right-angled triangle ABC, the hypotenuse AB is 12 centimeters and the angle A is 60 ‘CD is the height dropped from the vertex of the right angle C to the hypotenuse AB. find the length of the segment AD.

1. We calculate the length of the leg BC of the right-angled triangle ABC through the sine A:

BC / AB = sinus ∠A.

Sine 60 ° = √3 / 2.

BC = 12 x √3 / 2 = 6√3 centimeters.

2. Calculate the length of the AC leg of the AСD right-angled triangle:

AC = √AB² – BC² (by the Pythagorean theorem).

AC = √12² – (6√3) ² = √144 – 108 = √36 = 6 centimeters.

3. We calculate the length of the required segment of the blood pressure through the cosine ∠А.

AD / AC = cosine ∠A.

Cosine 60 ° = 1/2.

AD = 6 x 1/2 = 3 centimeters.

Answer: the length of the blood pressure segment is 3 centimeters.



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