In triangle XYZ, angle X = 90°, angle Y = 38°, and z = 4'5". Find y
To find side y in triangle XYZ, we can use the trigonometric function tangent (tan).
First, let's label the sides of the triangle:
- Side X is opposite to angle X.
- Side Y is opposite to angle Y.
- Side Z is the hypotenuse.
Since angle X is 90 degrees, we know that triangle XYZ is a right triangle. In a right triangle, the side opposite the right angle (in this case, side X) is called the hypotenuse.
Now, let's calculate y using tangents. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
tan(Y) = opposite/adjacent
In this case, tan(38°) = y/z
Since you mentioned that the value of z is 4'5", we need to convert that into inches. One foot is equal to 12 inches. So, 4'5" = 4 feet + 5 inches = 48 inches + 5 inches = 53 inches.
Now, we can substitute the given values into the formula:
tan(38°) = y/53
To solve for y, we multiply both sides of the equation by 53:
y = 53 * tan(38°)
Using a calculator, evaluate tan(38°) and multiply it by 53 to find the value of y. The result will be the length of side y in inches.