Question

В триугооьнике АВС угол С = 45 ,АВ=10 ,высота АД делит СВ на отрезки СД=8 и ВД =6 . Найти площадь АВС и высоту проведённую к стороне АВ

Answer 1

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Answer 2

Task: Finding the area of triangle ABC and the height drawn to side AB

To find the area of triangle ABC and the height drawn to side AB, we can use the given information about the triangle. Let's break down the steps:

1. Given information: - Angle C = 45 degrees - Side AB = 10 units - Segment SD = 8 units - Segment VD = 6 units

2. Finding the area of triangle ABC: - We can use the formula for the area of a triangle: Area = (base * height) / 2. - In this case, side AB is the base, and the height is the segment SD. - Plugging in the values, we get: Area = (10 * 8) / 2 = 40 square units.

3. Finding the height drawn to side AB: - To find the height drawn to side AB, we need to find the length of segment AD. - We can use the Pythagorean theorem to find the length of AD. - The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. - In this case, triangle ADB is a right triangle, with AB as the hypotenuse. - Using the Pythagorean theorem, we can find the length of AD: AD^2 = AB^2 - BD^2. - Since BD is equal to VD, we have: AD^2 = AB^2 - VD^2 = 10^2 - 6^2 = 100 - 36 = 64. - Taking the square root of both sides, we find: AD = 8 units.

4. Conclusion: - The area of triangle ABC is 40 square units. - The height drawn to side AB is 8 units.

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