the angle of elevation to a nearby tree from a point on the ground is measured to be $26^{\\circ}$. how tall…

the angle of elevation to a nearby tree from a point on the ground is measured to be $26^{\\circ}$. how tall is the tree if the point on the ground is 91 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

the angle of elevation to a nearby tree from a point on the ground is measured to be $26^{\\circ}$. how tall is the tree if the point on the ground is 91 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary.

Answer

Explanation:

Step1: Define trigonometric relation

We use the tangent function, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 26^\circ$, opposite side is tree height $x$, adjacent side is 91 feet. $\tan(26^\circ) = \frac{x}{91}$

Step2: Solve for $x$

Rearrange the equation to isolate $x$ by multiplying both sides by 91. $x = 91 \times \tan(26^\circ)$

Step3: Calculate the value

Use a calculator to find $\tan(26^\circ) \approx 0.4877$, then compute the product. $x \approx 91 \times 0.4877 = 44.3807$

Step4: Round to nearest tenth

Round the result to one decimal place. $x \approx 44.4$

Answer:

44.4 feet