Question

question
the angle of elevation to a nearby tree from a point on the ground is measured to be $54^{\circ}$. how tall is the tree if the point on the ground is 52 feet from the bottom of the tree? round your answer to the nearest hundredth of a foot if necessary.
answer attempt 2 out of 10
88.47
feet
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Explanation:

Step1: Define trigonometric relation

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta = 54^\circ$, adjacent side = 52 feet (distance from point to tree base), and opposite side = height of tree ($h$).

Step2: Rearrange to solve for $h$

$h = 52 \times \tan(54^\circ)$

Step3: Calculate the value

$\tan(54^\circ) \approx 1.3764$, so $h \approx 52 \times 1.3764 = 66.5728$

Step4: Round to nearest hundredth

$h \approx 66.57$

Answer:

66.57 feet