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MariettaO [177]
2 years ago
10

If the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle​

Mathematics
1 answer:
Murljashka [212]2 years ago
3 0
Answer: 80°

Step-by-Step Explanation:

By Angle Sum Property of a Triangle, all angles in a Triangle add up to 180°

Finding the Value of ‘x’ :-

2x + 3x + 4x = 180
5x + 4x = 180
9x = 180
x = 180/9
=> x = 20

Finding each Angle :-

2x = 2(20) = 2 * 20 = 40°
3x = 3(20) = 3 * 20 = 60°
4x = 4(20) = 4 * 20 = 80°

Hence, the Largest Angle is 80°
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Answer:

\bold{x =cos\theta}\\\bold{y=sin\theta}

Step-by-step explanation:

The given system of linear equations is:

(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0

We have to solve the equations for the values of x, y.

Let us use elimination method in which we eliminate one of the variables from the two variables.

For this, let us multiply the first equation by sin\theta and second equation by cos\theta

Now, the equations become:

(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)

Now, let us add (1) and (2):

(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta

Using the equation:

(-sin\theta)x+(cos\theta)y=0

Putting value of y:

\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta

So, the answer to the system of linear equations is:

\bold{x =cos\theta}\\\bold{y=sin\theta}

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