Chapter 10.6, Problem 43P

Error Analysis A student was finding the measure of an angle. The opposite side measured 6 cm and the hypotenuse measured 13 cm. His work is shown in the box to the right. Describe and correct the student’s error.

To determine

To describe and correct the students error

Answer to Problem 43P

The student calculated the wrong value, hence the correct value is ${27.5}^{\circ }$

Explanation of Solution

Given information:

A student was finding the measure of an angle and got opposite side as 6 cm and hypotenuse as 13 cm that is $\sin A=\frac{6}{13}$

Consider the diagram given in the question

Calculation:

At first calculate the value of $\sin A$

  $\begin{array}{l}\sin A=\frac{6}{13}\\ \sin A=0.461538461\\ A={\sin }^{-1}\left(0.461538461\right)\\ A={27.5}^{\circ }\end{array}$

The student calculated the value of $A$ as ${46}^{\circ }$ but the correct value is ${27.5}^{\circ }$