- A26°
- B29°
- C16°
- D32°
Step-by-Step Solution
Turn the cosine into a sine: cos°) = sin(90° − °)) = sin(116° − A). Equating the acute angles, ° − A, so ° and °. (Check: sin 87° = cos 3°.)
Answer: B) 29°
If sin = cos°), where is an acute angle, find A.
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.
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Introduction to Trigonometry practice questions
More Class 10 Introduction to Trigonometry practice
If tan 2A = cot(A − 18°), where 2A is an acute angle, find A.Find the value of tan 5° · tan 25° · tan 45° · tan 65° · tan 85°.For an acute angle θ, simplify √1 - ^2 θ/ ^2 θ.Simplify: (cosec θ − cot θ)(cosec θ + cot θ).For any angle θ, the expression (sin θ + cos θ)² + (sin θ − cos θ)² always equals: