Question

If the lenghts of the sides of a right triangle FGH are 8,15 and 17 and <7 is the smallest angle of the triangle, what is the numerical value of sin(2 14 years ago

Answer 1

<F*

Answer 2

Place the smallest angle vertex at the origin of an x-y cartesian coordinate system, the longer leg of the triangle lying om the positive x-axis. The right-angle vertex will be at (15,0) and the vertex of the larger acute angle will be at (15,8). Since 17 is the lemgth of the hypotenuse, 15 the length of the leg adjacent to the smaller angle, and 8 is the length of the leg oppositr the smaller acute angle, call its angle measure f, we have, by definition of the basic trig functions, that
sin(f) = 8/17, and cos(f) = 15/17. The double-angle identity for the sine function tells us that
sin(2f) = 2 sin(f) cos(f) = 2(8/17)(15/17)
= 240/289, which, to four significant figures, approximates to 0.8304.