Chapter 9.10, Problem 9PSB

To determine

To find:The angles of the given right-angle triangle to the nearest degree.

Answer to Problem 9PSB

The angles are ${37}^0$ , ${53}^0$ and ${90}^0$

Explanation of Solution

Given information:The sides of the triangle are given to be $3$ , $4$ and $5$

Formula used:Basic sine definitions have been used

Calculation:We know that the side with measure equal to $5$ will be hypotenuse of the triangle.

Hence, we find the sine and cosine inverses to find the value of the angels contained in the triangle

Thus, we assume the angles to be x , y and ${90}^0$ each. Hence, we can say that

  $x={\sin }^{-1}\frac{3}{5}$ , and

  $y={\sin }^{-1}\frac{4}{5}$

Thus, from the table of trigonometric values, we can say that

  $x={36.87}^0$ and

  $y={53.13}^0$

Thus, rounding off to the nearest degree, we get

  $x={37}^0$ and

  $y={53}^0$