Question

1. a child lies on the ground and looks up at the top of a 14-ft tree nearby. the child is 7 ft away from the tree. what is the angle of elevation from the child to the top of the tree? round to the nearest whole degree. 30° 14° 28° 63°

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right triangle where the height of the tree (opposite side to the angle of elevation) is \( 14 \) ft and the distance from the child to the tree (adjacent side) is \( 7 \) ft. We use the tangent function, which is defined as \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(\theta)=\frac{14}{7} = 2 \).

Step2: Calculate the angle of elevation

To find \( \theta \), we take the arctangent (inverse tangent) of \( 2 \). Using a calculator, \( \theta=\arctan(2) \). Calculating this, we get \( \theta\approx 63.43^\circ \), which rounds to \( 63^\circ \) when rounded to the nearest whole degree.

Answer:

\( 63^\circ \) (the option corresponding to \( 63^\circ \))