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Some Applications Of Trigonometry
EXAMPLES
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Step-by-Step Solution
Key Concept: Use the definition of the tangent function in a right‑angled triangle: \(\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}\). Here the opposite side is the height of the tower and the adjacent side is the horizontal distance (15 m).
1. Draw a right‑angled triangle: - The foot of the tower, the point on the ground, and the top of the tower form a right‑angled triangle. - Let \(h\) be the height of the tower (opposite side). - The distance from the point to the foot of the tower is given as \(15\) m (adjacent side). - The angle of elevation at the point is \(\theta = 60^{\circ}\).
2. Apply the definition of tangent: $$\tan 60^{\circ} = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{15}$$
3. Use the known value \(\tan 60^{\circ} = \sqrt{3}\): $$\sqrt{3} = \frac{h}{15}$$