Question

У трикутнику АВС АВ=ВС=6см, угол А=75°. Знайдіть висоту АD.​

Answer 1

Ответ: Высота AD=3 сантиметрам. Рада была помочь

Answer 2

To find the height AD in triangle ABC, you can use trigonometry and the properties of a right triangle. Here's how you can do it step by step:

Step 1: Draw the triangle ABC with the given information. Label the height AD and any other relevant angles or sides.

Step 2: Since AV = VC = 6 cm, triangle ABC is an isosceles triangle, which means that angles AVB and VBC are equal. Since the sum of all angles in a triangle is 180°, you can find the value of angle VBC.

Angle VBC = (180° - Angle AVB) / 2 Angle VBC = (180° - 75°) / 2 Angle VBC = 105° / 2 Angle VBC = 52.5°

Step 3: Now, consider the right triangle ABD. Angle ADB is a right angle (90°) because AD is the height to the base BC, and height is always perpendicular to the base.

Step 4: Since we know two angles in triangle ABD, we can find the third one: Angle ABD = 180° - Angle ADB - Angle BAD Angle ABD = 180° - 90° - 52.5° Angle ABD = 37.5°

Step 5: Now, we can use the tangent function to find the height AD.

tan(ABD) = AD / AB

Since AB = BC = 6 cm, we have:

tan(37.5°) = AD / 6

Now, solve for AD:

AD = 6 * tan(37.5°) AD ≈ 6 * 0.7536 AD ≈ 4.52 cm

So, the height AD is approximately 4.52 cm.