A student found the measure of ∠ A in an incorrect way. We will try to find the angle by ourselves so that we can determine error. Since we are given the opposite side of the angle and the hypotenuse of the right triangle, we can use the sine function to find the angle.
sin θ = Opposite side/Hypotenuse
Let's substitute the opposite side= 4.5 and the hypotenuse= 5 into the sine function, then try to simplify the equation for sin A.
Now we will find the angle which has a sine value of 0.9. To do so we need to write the inverse sine function by interchanging A and 0.9.
sin^(-1) ( 0.9)= A
Now we will calculate this value by using a graphing calculator. First we need to use the MODE button and change Radian to Degree to get the answer in degrees. Then we will push the 2nd and sin buttons to write the inverse sine function. Let's do it!
As we can see from the second calculator screen, we need to enter the inverse sine key by using 2nd and sin buttons. However, the student pushed just the sin button and then calculated the value for sin(0.9). Therefore, the correct measure of ∠ A is about 64.15806724^(∘).
