Math - High School Math

Trig_id

What is $\theta$ if and ?

$51.34^{\circ}$

$53.14^{\circ}$

$55.14^{\circ}$

$0.90^{\circ}$

$89.60^{\circ}$

Explanation

In order to find $\theta$ we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the $\tan$ of $\theta$ and its measure in degrees by utilizing the $\arctan$ function.

$\tan=\frac{opposite}{adjacent}$

$\tan=\frac{10}{8}$

$\tan=1.25$

Now to find the measure of the angle using the $\arctan$ function.

$\theta=\arctan1.25$

$\rightarrow 51.34^{\circ}$

If you calculated the angle's measure to be $0.90^{\circ}}$ then your calculator was set to radians and needs to be set on degrees.

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

What is the circumference of a circle with a radius of ?

$30\pi$

$15\pi$

Explanation

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding $C=2(\pi)(15)$

We multiply to find the value for the circumference is $30\pi$ .

The answer is $30\pi$ .

To the nearest tenth, give the area of a circle with diameter $7 \frac{1}{2}$ inches.

$44.2 \textrm{ in}^{2}$

$88.4 \textrm{ in}^{2}$

$22.1 \textrm{ in}^{2}$

$176.7 \textrm{ in}^{2}$

$56.3 \textrm{ in}^{2}$

Explanation

The radius of a circle with diameter $7 \frac{1}{2}$ inches is half that, or $3 \frac{3}{4} = 3.75$ inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 3.75^{2} \approx 44.2 \textrm{ in}^{2}$

What is the area of a rectangle with a length of and a width of ?

Explanation

The area of a rectangle is the length times the width:

Plug in our given values and solve:

How many radians are in $270^\circ$ ?

$\frac{3\pi}{2}$

$2\pi$

$\pi$

$\frac{2\pi}{3}$

$\frac{5\pi}{2}$

Explanation

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{270^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$270^\circ*\pi=180^\circ*x$

Isolate :

$\frac{270^\circ}{180^\circ}\pi=x$

$\frac{3\pi}{2}=x$

What is the perimeter of a triangle with side lengths of , , and ?

Explanation

To find the perimeter of a triangle you must add the three side lengths together.

In this case our equation would look like

Add the numbers together to get the answer .

What is the circumference of a circle with a radius of ?

$70\pi$

$35\pi$

$1225\pi$

Explanation

To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is

We then plug in the number for the radius into the equation yielding

$C=2(35)(\pi)$

We multiply to find the value for the circumference is $70\pi$ .

The answer is $70\pi$ .

Solve for :

$\sqrt{x^2+12x+36} =4$

$x = \left { -10, -2\right }$

Explanation

To solve for in the equation $\sqrt{x^2+12x+36} =4$

Square both sides of the equation

$\rightarrow (\sqrt{x^2+12x+36})^2 =(4)^2$

$\rightarrow x^2+12x+36 =16$

Set the equation equal to by subtracting the constant from both sides of the equation.

$\rightarrow (x^2+12x+36) - 16 =(16) -16$

$\rightarrow x^2+12x+20 =0$

Factor to find the zeros:

$\rightarrow (x+10)(x+2) = 0$

This gives the solutions

$x = \left { -10, -2\right }$ .

Verify that these work in the original equation by substituting them in for . This is especially important to do in equations involving radicals to ensure no imaginary numbers (square roots of negative numbers) are created.