If tanA = 3⁄4, then what is the value of sinA?
- (a)3⁄5
- (b)4⁄5
- (c)5⁄3
- (d)1
Answer
Why
Correct — A. Read tan A = 3⁄4 as opposite ⁄ adjacent in a right triangle.
Opposite = 3, adjacent = 4
Hypotenuse = √(3² + 4²) = √25 = 5
sin A = opposite ⁄ hypotenuse = 3⁄5 → option (a)
Why the others are wrong
- (b)4⁄5 — 4⁄5 is adjacent ⁄ hypotenuse, which is cos A. If sin A were 4⁄5, tan A would be 4⁄3, not 3⁄4.
- (c)5⁄3 — 5⁄3 is hypotenuse ⁄ opposite, which is cosec A. A sine can never exceed 1, so 5⁄3 is impossible for sin A.
- (d)1 — 1 is sin 90°, where tan is undefined. Since tan A = 3⁄4 is below 1, A is under 45° and sin A is under 0.71.
Concept
In a right triangle, sin = opposite ⁄ hypotenuse, cos = adjacent ⁄ hypotenuse and tan = opposite ⁄ adjacent. Given one ratio, draw the triangle, find the missing side with Pythagoras and read off any other ratio.
3, 4, 5 is a Pythagorean triple, so tan A = 3⁄4 gives sin A = 3⁄5 and cos A = 4⁄5 at once.
The stem does not say A is acute. tan A is also 3⁄4 in the third quadrant, where sin A = −3⁄5. That value is not offered, so the key reads A as an acute angle of a right triangle.
Key facts
- sin A = opposite ⁄ hypotenuse, cos A = adjacent ⁄ hypotenuse, tan A = opposite ⁄ adjacent.
- sin²A + cos²A = 1. Here (3⁄5)² + (4⁄5)² = 9⁄25 + 16⁄25 = 1.
- tan A = sin A ⁄ cos A = (3⁄5) ⁄ (4⁄5) = 3⁄4.
- For any angle, −1 ≤ sin A ≤ 1.
Study next
Common traps
- Swapping opposite and adjacent, which gives cos A = 4⁄5 instead of sin A.
- Writing hypotenuse ⁄ opposite (5⁄3), the reciprocal of sin A.
26 Sep 2025, 16:00, Quant Q.24 asks the same question, tan A = 3⁄4, and keys sin A = 3⁄5.
19 Sep 2025, 09:00, Quant Q.22 starts from sin x = 3⁄5 with x acute, so tan x = 3⁄4 and (1 + tan x)⁄(1 − tan x) keys 7. 23 Sep 2025, 16:00, Quant Q.18 puts A in the second quadrant and keys tan A = −3⁄4.
Related PYQs
No directly related past PYQ was found.