Question

дві сторони трикутника дорівнюють 16 і 18 см, а кут між ними 60 градусів. Знайдіть висоти, проведені до цих сторін

Answer 1

Ответ:

9√3 см, 8√3 см.

Объяснение:

Пусть в △АВС АL и CK - высоты, AB=16 см, ВС=18 см, <B=60°.

В прямоугольном △ALB <ALB=90°, sinABL=AL/AB; => AL=AB*sin60°=16*√3/2=8√3 см.

В прямоугольном △СKB <CKB=90°, sinCBK=CK/BC; => CK=BC*sin60°=18*√3/2=9√3 см.

Answer 2

Given Information

We are given that two sides of a triangle measure 16 cm and 18 cm, and the angle between them is 60 degrees.

Solution

To find the heights drawn to these sides, we can use the formula for the area of a triangle. The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

In this case, the base of the triangle will be one of the given sides, and the corresponding height will be the height drawn to that side.

Let's denote the sides of the triangle as follows: - Side A = 16 cm - Side B = 18 cm

To find the height drawn to side A, we need to know the length of side B. Similarly, to find the height drawn to side B, we need to know the length of side A.

To find the missing side, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we know side A, side B, and the angle between them (60 degrees). We can use the Law of Cosines to find the missing side.

Let's calculate the missing side using the Law of Cosines:

Side C^2 = Side A^2 + Side B^2 - 2 * Side A * Side B * cos(60 degrees)

Side C^2 = 16^2 + 18^2 - 2 * 16 * 18 * cos(60 degrees)

Now, we can calculate the value of Side C:

Side C = sqrt(Side C^2)

Once we have the value of Side C, we can calculate the heights drawn to sides A and B using the formula for the area of a triangle.

Let's calculate the missing side and the heights drawn to sides A and B:

Side C = sqrt(16^2 + 18^2 - 2 * 16 * 18 * cos(60 degrees))

Height to Side A = (2 * Area) / Side A

Height to Side B = (2 * Area) / Side B

Calculation

Let's calculate the missing side and the heights drawn to sides A and B:

Side C = sqrt(16^2 + 18^2 - 2 * 16 * 18 * cos(60 degrees))

Side C = sqrt(256 + 324 - 576 * 0.5)

Side C = sqrt(256 + 324 - 288)

Side C = sqrt(292)

Side C ≈ 17.088 cm

Now, let's calculate the heights drawn to sides A and B:

Height to Side A = (2 * Area) / Side A

Height to Side B = (2 * Area) / Side B

Since we don't have the area of the triangle, we cannot calculate the exact heights drawn to sides A and B without additional information.

Please provide the area of the triangle, or any additional information, if available, so that we can calculate the heights accurately.