Trigonometric Word problems - Ottawa, Ontario, Canada | Raise My Marks - Free Printable

We are given a trigonometric word problem involving the angle of elevation and need to find the height of a tree using right triangle trigonometry.

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🔹 Problem Statement:

From a point on the ground 47 feet from the foot of a tree, the angle of elevation to the top of the tree is 35°. Find the height of the tree.

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🔹 Diagram Analysis:

The diagram shows a right triangle $ \triangle ABC $, where:
- Point $ C $ is at the base of the tree.
- Point $ B $ is the top of the tree.
- Point $ A $ is the observation point on the ground, 47 feet from the tree.
- $ \angle A = 35^\circ $
- $ AC = 47 $ ft (adjacent side)
- $ BC = x $ ft (opposite side) — this is the height of the tree, which we want to find.
- $ \angle C = 90^\circ $

So, we have a right triangle with:
- Adjacent side = 47 ft
- Angle = 35°
- Opposite side = $ x $ (unknown)

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🔹 Use Tangent Function:

In a right triangle:
$$
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
$$

Here:
$$
\tan(35^\circ) = \frac{x}{47}
$$

Now solve for $ x $:
$$
x = 47 \cdot \tan(35^\circ)
$$

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🔹 Calculate:

Using a calculator:
$$
\tan(35^\circ) \approx 0.7002
$$

So:
$$
x = 47 \cdot 0.7002 \approx 32.9094
$$

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🔹 Final Answer:

$$
\boxed{32.9} \text{ feet (approximately)}
$$

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✔ Conclusion:

The height of the tree is approximately 32.9 feet.

> 💡 Tip: Always round to a reasonable number of significant figures. Since 47 has two significant figures and 35° is exact, rounding to 33 feet might be acceptable depending on context. But if more precision is desired, 32.9 ft is fine.

Let me know if you'd like it rounded differently!