Find the value of x in each right triangle.
A.)
short leg= 8
hyp= x
and one angle equals 42
B.)
short leg= 12
long leg= x
and one angle equals 67
please help!!! i have a final tomorrow
To find the value of x in each right triangle, we can use the trigonometric ratios of sine, cosine, and tangent.
A.) In triangle A, we have the short leg = 8, the hypotenuse = x, and one angle = 42 degrees.
Using the trigonometric ratio of sine (sin), we have sin(angle) = opposite/hypotenuse. In this case, the angle is 42 degrees. The opposite side is the short leg (8), and the hypotenuse is x.
So, sin(42) = 8/x. To find x, we can rearrange the equation as x = 8 / sin(42).
To calculate x, evaluate sin(42) using a scientific calculator or online trigonometric calculator. Once you have the sine value, substitute it into the equation x = 8 / sin(42) to find the value of x.
B.) In triangle B, we have the short leg = 12, the long leg = x, and one angle = 67 degrees.
Using the trigonometric ratio of cosine (cos), we have cos(angle) = adjacent/hypotenuse. In this case, the angle is 67 degrees. The adjacent side is the short leg (12), and the hypotenuse is x.
So, cos(67) = 12/x. To find x, rearrange the equation as x = 12 / cos(67).
Evaluate cos(67) using a scientific calculator or online trigonometric calculator. Then substitute it into the equation x = 12 / cos(67) to find the value of x.
Remember to double-check your calculations, and be sure to use the correct trigonometric ratios for each triangle.