- A30°
- B20°
- C45°
- D60°
Step-by-Step Solution
Shadow m. The ramp runs m, so .
Answer: A) 30°
A sun ray at 60° to the ground just grazes the top of a 1.5 m wall and reaches the ground at the shadow's tip. A ramp from the top of the wall meets the ground 3 times as far from the wall as the shadow's tip. Find the angle the ramp makes with the ground (marked ?).
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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