Question

when the suns rays are at an angle of 39°, the distance from the top of dakotas head to the tip of her shadow is 77 inches. about how tall is dakota? round your answer to the nearest inch if necessary. enter your response in the field.

Explanation:

Step1: Identify trigonometric relation

We use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta = 39^{\circ}$, the hypotenuse is 77 inches and the opposite side is Dakota's height $h$.

Step2: Set up the equation

$\sin(39^{\circ})=\frac{h}{77}$.

Step3: Solve for $h$

$h = 77\times\sin(39^{\circ})$.
We know that $\sin(39^{\circ})\approx0.6293$. So $h=77\times0.6293 = 48.4561\approx48$ inches.

Answer:

48 inches