- A21/29
- B20/29
- C20/21
- D21/20
Step-by-Step Solution
Total rise cm, total run cm, so the line is cm. (one step alone gives the same ratio).
Answer: A) 21/29
A staircase has 5 equal steps, each 20 cm high and 21 cm deep. The orange line through the corners of the steps makes an angle θ with the floor. Find cos θ.
Class 10Introduction to TrigonometryTrigonometry
Key idea: Why ratios — and not lengths
Two right triangles with the same acute angle θ are SIMILAR (Class 10 ch. 6 — AA criterion: both have a right angle and the angle θ).
Similar triangles → corresponding sides in fixed ratio.
So the ratio (opposite / hypotenuse) takes the SAME value in any right triangle with angle θ — regardless of how big the triangle is.
That's why sin θ, cos θ, tan θ are FUNCTIONS of the angle alone — they're well-defined.
This is the fundamental reason trigonometry works as a clean theory.
Similar triangles → corresponding sides in fixed ratio.
So the ratio (opposite / hypotenuse) takes the SAME value in any right triangle with angle θ — regardless of how big the triangle is.
That's why sin θ, cos θ, tan θ are FUNCTIONS of the angle alone — they're well-defined.
This is the fundamental reason trigonometry works as a clean theory.
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