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 have a right - triangle where the hypotenuse is 77 inches and we want to find the side opposite the 39° angle. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 39^{\circ}$, the hypotenuse $c = 77$ inches, and the opposite side is Dakota's height $h$. So, $\sin(39^{\circ})=\frac{h}{77}$.

Step2: Solve for $h$

We can rewrite the equation as $h = 77\times\sin(39^{\circ})$. We know that $\sin(39^{\circ})\approx0.6293$. Then $h=77\times0.6293$.
$h = 77\times0.6293=48.4561$.

Step3: Round the result

Rounding 48.4561 to the nearest inch gives 48 inches.

Answer:

48 inches