Error: The student's mistake was to use the inverse function for sine. Correct Answer: ≈ 9.2 centimeters
Practice makes perfect
We are told that one of the angles in a right triangle measures 0.45 radians. We also know that the side opposite to the angle measure 4 centimeters. Let's draw the triangle!
A student found the length of the hypotenuse by using the following procedure.
To identify the mistake, we will find the length of the hypotenuse by using the trigonometric ratio for sine.
sin θ = Opposite/Hypotenuse
In our case, the length of the opposite side is 4, the length of the hypotenuse is x, and the measure of the angle is 0.45 radians.
sin θ = Opposite/Hypotenuse ⇒
sin 0.45 = 4/x
Now, we will solve this equation to find the length of the hypotenuse x.
As we can see, to solve the equation for x we need to divide both sides by sin 0.45. This means that the student's mistake was to use the inverse sine function instead of using the division.
4/sin 0.45 ≠ 4 sin^(- 1) 0.45
Having described the mistake, we can calculate the correct length of the hypotenuse. Remember that we are still working with radians.
