Mathematics College

what is the value of x in the triangle

What Is The Value Of X In The Triangle

Answers

Answer 1

Answer:

7

Step-by-step explanation:

In an 30-60-90 right triangle, the longer leg is the shorter leg multiplied by [tex]\sqrt{3}[/tex]

So [tex]7\sqrt{3} =x*\sqrt{3[/tex]

[tex]7=x[/tex]

x=7

Answer 2

Answer:

A. 21

Step-by-step explanation:

This is a 30-60-90 triangle, where you have one 30° angle, one 60°, and one 90° (aka right) angle.  

The sides of a 30-60-90 triangle adhere to the following rules:

The side opposite the 30° angle is the shortest side and we can call its length "x".The side opposite the 60° angle is the medium length side and its length is given by x * √3.  This means its length is the product of the length of the side opposite the 30° angle and √3.The side opposite the 90° (right) angle is the longest side (aka the hypotenuse) and its length is given by 2x.  This means its length is twice the length of the side opposite the 30° angle.

Since 7√3 is the length of the side opposite the 30° angle, the entire expression represents x.

Since the length of the side opposite the 60° angle is given by x * √3, the length of this side is (7√3)(√3).

Simplifying gives us 7*3, which is 21.

Thus, the value of x in the triangle is 21 (answer choice A.)

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Answers

Given the equation f(x) = a · bx where a and b are constants. So, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

To find the equation of transformed function g in terms of function f is explained below: If f(x) = a · bx, then the transformed function g(x) can be represented by g(x) = a · bx + h, where h is the vertical shift (if h > 0, the graph shifts upward, and if h < 0, the graph shifts downward).

Now, we have to replace the value of 'a' to complete the equation of g(x). But, we don't have any value of 'a' provided in the question. Hence, we can't determine the equation of transformed function g in terms of function f for the given information.

Next, let's move to the trigonometric function. It is given that: R S 9 sin cos tan sin cos tan-¹ /ASin, Cos, Tan, Cosec, Sec, and Cot are six trigonometric functions. Let's see their definitions and their corresponding inverse functions:

1. Sine: It is defined as the ratio of the length of the side opposite the given angle to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is sin⁻¹.

2. Cosine: It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. Its corresponding inverse function is cos⁻¹.

3. Tangent: It is defined as the ratio of the length of the side opposite the given angle to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is tan⁻¹.

4. Cosecant: It is defined as the ratio of the length of the hypotenuse to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cosec⁻¹.

5. Secant: It is defined as the ratio of the length of the hypotenuse to the length of the adjacent side in a right-angled triangle. Its corresponding inverse function is sec⁻¹.

6. Cotangent: It is defined as the ratio of the length of the adjacent side to the length of the side opposite the given angle in a right-angled triangle. Its corresponding inverse function is cot⁻¹.

Hence, the answer to the given problem is g(x) = a · bx + h, and the explanation of the trigonometric function.

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