follow the steps to find the area of the shaded region. next, find the height (h) of the triangle inside the…

follow the steps to find the area of the shaded region. next, find the height (h) of the triangle inside the sector. hint: use sohcahtoa h = ? cm round to four decimal places.

follow the steps to find the area of the shaded region. next, find the height (h) of the triangle inside the sector. hint: use sohcahtoa h = ? cm round to four decimal places.

Answer

Explanation:

Step1: Identify the trig - function to use

We know the hypotenuse of the right - triangle is $r = 14$ cm and we want to find the height $h$ with respect to the given angle $\theta=46^{\circ}$. Using the sine function from SOHCAHTOA (Sine = Opposite / Hypotenuse), where the height $h$ is the opposite side to the angle $\theta$.

Step2: Apply the sine formula

The formula for sine is $\sin\theta=\frac{h}{r}$. We can solve for $h$ by multiplying both sides of the equation by $r$. So $h = r\sin\theta$. Substitute $r = 14$ cm and $\theta = 46^{\circ}$ into the formula. First, make sure your calculator is in degree mode. Then $h=14\times\sin(46^{\circ})$. $h = 14\times0.7193398 = 10.0707572$.

Step3: Round the result

Rounding to four decimal places, $h\approx10.0708$ cm.

Answer:

$10.0708$