Question

Один из углов треугольника равен 60 градусов, а сумма длин гипотенузы и меньшего катета равна 28,2 см. Найдите длину гипотенузы треугольника. Решить с объяснением!!!! не только решение, но и объяснение!!!!

Answer 1

Решение :
1)Так как  треугольник прямоугольный и один из его углов 60⁰ , тогда другой острый угол 90⁰-60⁰=30⁰. А катет , лежащий напротив угла в 30⁰ ,равен половине гипотенузы.
2)Пусть этот катет х см, тогда гипотенуза 2х. Решим уравнение
 х+2х=28,2
3х=28,2
х=28,2:3
х=9,4
3) 9,4 см - это катет
2·9,4=18,8 см - это гипотенуза
Ответ: 18,8 см
    

Answer 2

Given Information:

We are given that one of the angles of the triangle is 60 degrees and the sum of the length of the hypotenuse and the shorter leg is 28.2 cm.

Approach:

To find the length of the hypotenuse, we can use the trigonometric relationship between the sides and angles of a right triangle. Specifically, we can use the cosine function.

Let's assume that the shorter leg of the triangle is denoted by 'a' and the hypotenuse is denoted by 'c'. We are given that the sum of 'a' and 'c' is 28.2 cm.

Using the cosine function, we can write the equation as follows:

cos(60) = a/c

Simplifying the equation, we have:

a = c * cos(60)

Substituting the value of 'a' from the given equation, we get:

c * cos(60) + c = 28.2

Now, we can solve this equation to find the value of 'c'.

Solution:

Let's solve the equation to find the length of the hypotenuse 'c'.

c * cos(60) + c = 28.2

Using the value of cos(60) = 0.5, we can rewrite the equation as:

0.5c + c = 28.2

Simplifying the equation, we have:

1.5c = 28.2

Dividing both sides of the equation by 1.5, we get:

c = 28.2 / 1.5

Calculating the value, we find:

c ≈ 18.8 cm

Therefore, the length of the hypotenuse of the triangle is approximately 18.8 cm.

Explanation:

The given triangle is a right triangle, which means it has one angle measuring 90 degrees. We are given that one of the angles is 60 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can find the third angle by subtracting the sum of the other two angles from 180 degrees.

Third angle = 180 - (90 + 60) = 30 degrees

Now, we have the measures of all three angles of the triangle: 90 degrees, 60 degrees, and 30 degrees.

Using the trigonometric relationship between the sides and angles of a right triangle, we can determine the length of the hypotenuse. The cosine function relates the adjacent side (the shorter leg) and the hypotenuse.

cos(60) = adjacent/hypotenuse

Since we are given the sum of the length of the hypotenuse and the shorter leg, we can substitute the value of the adjacent side (a) as (28.2 - c) in the equation.

cos(60) = (28.2 - c)/c

Simplifying the equation, we get:

c * cos(60) + c = 28.2

Solving this equation, we find the length of the hypotenuse (c) to be approximately 18.8 cm.

Please note that the solution is approximate due to rounding in the calculations.

Answer:

The length of the hypotenuse of the triangle is approximately 18.8 cm.