Question

leah knows that her high school building is 44 feet tall. she looks up at an angle of 71.2 degrees to the top of her high school building. how far away from the base of her high school building is she standing to the nearest foot?

Explanation:

Step1: Define trigonometric relationship

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 71.2^\circ$, opposite side (building height) $= 44$ ft, adjacent side (distance to building) $= x$.

Step2: Rearrange to solve for $x$

Isolate $x$ using the rearranged formula: $x = \frac{\text{opposite}}{\tan(\theta)}$

Step3: Substitute values and calculate

Substitute the known values:
$x = \frac{44}{\tan(71.2^\circ)}$
Calculate $\tan(71.2^\circ) \approx 2.923$, so $x \approx \frac{44}{2.923} \approx 15.05$

Step4: Round to nearest foot

Round $15.05$ to the nearest whole number.

Answer:

15 feet