Question

В прямоугольном треугольнике один из катетов равен 17 кв корень из 3, угол, лежащий напротив него равен 60 градусам, а гипотенуза равна 34 .Найдите площадь треугольника. напишите решение плиз,очень надо

Answer 1

Если я правильно поняла,  катет  равен $17\sqrt{3}$ ?
Прямой угол А, катет АВ 17 корней из 3, угол С равен 60 градусам, гипотенуза ВС 34. найти 
найти площадь тр. АВС.
Площадь равна половине  произведения его катетов: 1/2 АВ*АС
Угол В  90-60 = 30. Катет который лежит напротив угла в 30 градусов, равен половине гипотенузы АС=$\frac{1}{2}$ВС, АС=17. Можно найти АС и по теореме Пифагора.
Подставляй теперь в первую формулу всё, и вычисляй. 

Answer 2

Problem Analysis

We are given a right triangle with one leg measuring 17√3, an angle opposite that leg measuring 60 degrees, and the hypotenuse measuring 34. We need to find the area of the triangle.

Solution

To find the area of the triangle, we can use the formula: Area = (1/2) * base * height.

In a right triangle, the base and height are the two legs. Since we know one leg is 17√3, we can use that as the base. To find the height, we can use the trigonometric relationship between the angle and the sides of a right triangle.

The trigonometric relationship for a right triangle is: sin(angle) = opposite/hypotenuse.

In this case, the angle is 60 degrees, the opposite side is the height, and the hypotenuse is 34. We can rearrange the equation to solve for the height:

height = sin(angle) * hypotenuse

Now we have all the information we need to calculate the area of the triangle.

Calculation

Let's calculate the height first: height = sin(60 degrees) * 34

Using a calculator, we find that sin(60 degrees) is equal to √3/2. Substituting this value into the equation, we get: height = (√3/2) * 34

Simplifying, we have: height = 17√3

Now we can calculate the area of the triangle: Area = (1/2) * base * height Area = (1/2) * 17√3 * 17√3 Area = (1/2) * 17 * 17 * 3 Area = 289 * 3 Area = 867

Therefore, the area of the triangle is 867 square units.

Answer

The area of the triangle is 867 square units.

Note: The sources provided did not contain specific information related to this problem. The solution provided is based on the principles of trigonometry and the formula for the area of a triangle.