Help with math problems?

It is very easy if you know trigonometry. The sine of an angle in a right triangle (the angle must be one of the acute angles in the right triangle) is the ratio of the length of the opposite side of the angle and the length of the hypotenuse of the triangle.

Now, it will be easier for you to understand if you draw the triangle XYZ in a paper.

For the first question, sin (Angle X) = ZY/XY

Or, sin (30 degrees) = X/Z

Or, 1/2 = X/10

Henceforth, X = 5.

Now, for the second question, sin (Angle X) = ZY/XY

Or, sin (Angle X) = 7/15

Henceforth, Angle X = arcsin (7/15) = 27.818 degrees (approximately)

You can get the value of arcsing of any number by using a calculator which I did in this case. Otherwise, you know that 7/15 = 0.5 approximately and the sin of 30 degrees is 0.5. So the arcsin of 7/15, i.e., of 0.5 (approximately) is 30 degrees (approximately) but that won't be a good approximation.

N.B. sin (30 degrees) = 1/2 = 0.5

If X = 30, then Y = 60.

A 30-60-90 triangle has side measurements n-sqrt(3) * n-2n, where n is opposite the smallest angle. Since X is the smaller angle, x is the smaller leg. z is the side opposite the right angle, or the 2n side, so 10 = 2n, and x = n. So x = 5. y = 5sqrt(3), by the way.

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x is the side opposite X, and z is the side opposite the right angle, or the hypotenuse. So 7/15 is opp/hyp, or sin(X).

arcsin(7/15) = 27.8º

we knew that , sinx/x=siny/y =sinz/z

a) so, sin 30/x =sin90/10

so x= 1

b) sinX/7 =sin90/15

so , X =27.81 deg