Question

ABCD is a rectangle, and ∠OAB is perpendicular to OB,BC=2cm, DC=6cm, and tanx°= 3/4 . Find sinx° and cosx°.

A. sinx°=3/5, cosx°=4/5
B. sinx°= 4/5 , cosx°=3/5
C. Both a and b
D. None of the above

Answer 1

Given tanx° = 3/4 in a right-angled triangle, the opposite side is 3 units, and the adjacent side is 4 units, which makes the hypotenuse 5 units long. Thus, sinx° is 3/5 and cosx° is 4/5, corresponding to option A.

Step-by-step explanation:

To find sinx° and cosx°, we must first realize that these values represent the ratios of the sides in a right-angled triangle. Given tanx° = 3/4, we can infer that the side opposite to angle x has a length of 3 units, and the adjacent side has a length of 4 units. Using the Pythagorean theorem, the hypotenuse (h) of the triangle is found by the equation h² = 3² + 4², which yields h = 5. Therefore, sinx° = opposite/hypotenuse = 3/5, and cosx° = adjacent/hypotenuse = 4/5. So, the correct answer would be option A: sinx°=3/5, cosx°=4/5.