All of it plus the triangle diagram in the description of all trigonometry

Question

ScanSolve AI Tutor · Accepted Answer

SOH CAH TOA is a mnemonic used to remember the definitions of the three basic trigonometric ratios for a right-angled triangle.

Consider a right-angled triangle with an angle $\theta$ :

      /|
     / |
    /  | Opposite
   /   |
  /____|
 Hypotenuse  Adjacent

\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}

\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}

\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}

Now, let's solve for $x$ using the previous problem's context:

Identify the knowns and unknowns from the problem.
The given angle is $\theta = 30^\circ$ .
The side opposite the $30^\circ$ angle is $x$ .
The hypotenuse is 10.
Choose the appropriate trigonometric ratio.
Since we have the Opposite side and the Hypotenuse, we use the Sine ratio (SOH).
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$
Substitute the values into the formula.
$\sin(30^\circ) = \frac{x}{10}$
Solve for $x$ .
We know that $\sin(30^\circ) = 0.5$ .
$0.5 = \frac{x}{10}$
Multiply both sides by 10:
$x = 0.5 \times 10$ $x = 5$
The value of $x$ is $\boxed{5}$ .

Answer