Using tan ratio for heights
Using the tan ratio for heights means using tan theta = opposite side / adjacent side in a right triangle to relate height and horizontal distance.
Practice This ConceptMain explanation
Teacher explanation
In many class 10 questions, we know the horizontal distance and the angle of elevation or depression. Then the tangent ratio is most useful because it connects the vertical height with the horizontal distance directly. If the angle is theta, tan theta equals the height or opposite side divided by the horizontal or adjacent side. This is the most common ratio in tower, tree, and building problems.
Example
If a tower is seen from 30 m away at an angle of elevation of 45 degrees, then tan 45 = height/30, so the height becomes 30 m.
Simple analogy
Tan links the top and the ground, so it is the height-distance ratio.
Common confusion
Students sometimes use sin or cos when only the height and horizontal distance are involved, or they swap opposite and adjacent sides.
Exam tip
If the question gives height and base distance, tan is usually the first ratio to test.
Answer writing and exam use
1-mark use
Write the exact meaning of using tan ratio for heights in one clean line.
2-mark use
Define using tan ratio for heights and add one example or condition.
3-mark use
Explain using tan ratio for heights, show the method or example, and mention the common mistake.
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