Angle of elevation word problem examples

📚 Quick Study Guide

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• Definition: Angle of elevation is the angle from the horizontal upward to a line of sight from the observer to some point of interest.
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• Trigonometric Ratios: Remember the basic trigonometric ratios: Sine ($\sin = \frac{opposite}{hypotenuse}$), Cosine ($\cos = \frac{adjacent}{hypotenuse}$), and Tangent ($\tan = \frac{opposite}{adjacent}$). Tangent is most commonly used.
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• Solving Strategy: Draw a diagram representing the word problem. Label the known angles and sides. Identify the unknown you need to find. Select the appropriate trigonometric ratio, and solve for the unknown.
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• Example Formula: If you know the angle of elevation ($\theta$) and the adjacent side ($a$), and you want to find the opposite side ($o$), use: $\tan(\theta) = \frac{o}{a}$, which means $o = a \cdot \tan(\theta)$.

Practice Quiz

1. A kite is flying at an angle of elevation of 60°. The string holding the kite is 80 feet long. How high is the kite above the ground?
1. 40 ft
2. 40$\sqrt{3}$ ft
3. 80 ft
4. 80$\sqrt{3}$ ft
2. From a point on the ground 25 feet from the base of a tree, the angle of elevation to the top of the tree is 32°. Find the height of the tree.
1. 13.2 ft
2. 15.6 ft
3. 16.2 ft
4. 40.0 ft
3. A building is 50 feet high. A person looks at the top of the building with an angle of elevation of 70°. How far is the person from the base of the building?
1. 17.1 ft
2. 18.2 ft
3. 53.2 ft
4. 137.4 ft
4. A ladder leans against a wall, making an angle of 75° with the ground. If the foot of the ladder is 5 feet from the wall, how high up the wall does the ladder reach?
1. 5.2 ft
2. 18.7 ft
3. 19.3 ft
4. 20 ft
5. A surveyor stands 100 meters from the base of a radio tower. The angle of elevation to the top of the tower is 35°. Find the height of the tower.
1. 57.3 m
2. 70.0 m
3. 122.1 m
4. 142.8 m
6. An airplane is flying at an altitude of 3000 feet. The angle of elevation from the airport to the plane is 20°. What is the horizontal distance from the airport to the plane?
1. 1026 ft
2. 3192 ft
3. 8242 ft
4. 8772 ft
7. From the top of a cliff 80 meters high, the angle of elevation to a ship is 7°. How far is the ship from the base of the cliff?
1. 639 m
2. 649 m
3. 652 m
4. 659 m