Question

Find the value of x to the nearest degree

1. 83
2. 53
3. 67
4.22

Answer 1

In a right-angled triangle with a height of 3 and a hypotenuse of
`√(58)`, the angle x is approximately 22 degrees.

In a right-angled triangle, the relationship between the sides is given by the Pythagorean theorem:

`a^2+b^2=c^2`
where a and b are the legs of the right triangle and c is the hypotenuse.

In your case, the height (a) is given as 3, and the hypotenuse (c) is given as
`√(58)`.

So, the equation becomes:

`\begin{aligned}& 3^2+b^2=(√(58))^2 \\& 9+b^2=58\end{aligned}`

Now, solve for b:

`\begin{aligned}& b^2=58-9 \\& b^2=49 \\& b=√(49) \\& b=7\end{aligned}`

Now that you know the length of the other leg (b), you can find the angles using trigonometric ratios.

The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, for the angle x:

`\begin{aligned}& \tan (x)=\frac{\text { opposite }}{\text { adjacent }} \\& \tan (x)=(3)/(7)\end{aligned}`

Now, find the angle x using the arctangent (inverse tangent) function:

`x=\arctan \left((3)/(7)\right)`

Use a calculator to find the arctangent of
`(3)/(7)` and round the result to the nearest degree. The answer should be approximately 22 degrees.

So, the correct option is 4. 22 degrees.

Answer 2

x = 23

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side/ hypotenuse

sin x = 3 / sqrt(58)

take the inverse sin of each side

sin ^-1 (sin x) = sin ^-1( 3 / sqrt(58))

x = sin ^-1( 3 / sqrt(58))

x=23.19859051

To the nearest degree

x = 23