Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 20, 2023

Find the value of $x$ given the equation $\sin 30^{\circ} = \frac{x}{8}$ , and express the solution in its simplest form.

STEP 1

Assumptions1. We are solving for x in the equation $\sin30^{\circ}=\frac{x}{8}$ . We are using the standard mathematical convention where angles are measured in degrees

STEP 2

First, we need to know the value of $\sin30^{\circ}$ . From the standard trigonometric values, we know that $\sin30^{\circ} = \frac{1}{2}$ .

STEP 3

Substitute the value of $\sin30^{\circ}$ into the equation.
$\frac{1}{2} = \frac{x}{8}$

STEP 4

To solve for x, we need to isolate x. We can do this by multiplying both sides of the equation by8.
$8 \times \frac{1}{2} =8 \times \frac{x}{8}$

STEP 5

Perform the multiplication on both sides of the equation to solve for x.
$4 = x$ So, the solution to the equation $\sin30^{\circ}=\frac{x}{8}$ is $x =4$ .

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