For the acute angles in a right triangle, sin(3x+10°)=cos(x+24°)
. What is the value of x?
To solve this equation, we can use the fact that in a right triangle, the sine of an acute angle is equal to the cosine of the complement of that angle.
Therefore, we can rewrite the given equation as:
sin(3x + 10°) = sin(90° - (x + 24°))
Now, we know that sine is an odd function, so sin(x) = sin(-x). Therefore, we can rewrite the right side of the equation as:
sin(90° - (x + 24°)) = sin(66° - x)
Now, we have:
sin(3x + 10°) = sin(66° - x)
For two angles to have the same sine value, the angles must be equal or their sum must be equal to 180°. Therefore, we have:
3x + 10 = 66 - x
4x = 56
x = 14
Therefore, the value of x is 14°.