To find the height of the tree, we can use trigonometry. Specifically, we will use the tangent ratio because we know the angle and the side adjacent to it (the distance from the tree), and we want to find the side opposite to it (the height of the tree).
Step 1: Identify the knowns and the unknown.
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Angle of elevation: $35^\circ$
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Adjacent side (distance from base): $10$ feet
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Opposite side (height of tree): Let's call this $x$.
Step 2: Set up the equation.
The formula for tangent is:
$$ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} $$
Substitute our values into the formula:
$$ \tan(35^\circ) = \frac{x}{10} $$
Step 3: Solve for $x$.
To get $x$ by itself, multiply both sides by $10$:
$$ x = 10 \cdot \tan(35^\circ) $$
Now, calculate the value of $\tan(35^\circ)$. Using a calculator:
$$ \tan(35^\circ) \approx 0.7002 $$
Multiply this by $10$:
$$ x \approx 10 \cdot 0.7002 $$
$$ x \approx 7.002 $$
Rounding to one decimal place, the height is $7.0$ feet.
Final Answer: The height of the tree is approximately
7.0 feet.
Parent Tip: Review the logic above to help your child master the concept of right triangle trigonometry word problems worksheet.
