Question

In a right triangle, sin(β) = 0.292. If the hypotenuse of the triangle has a length of 17.5 cm, what is the length of the side adjacent to angle β. Note: You will also need to use the Pythagorean theorem to answer this question.

Answer 1

Solution

Step 1:

$\begin{gathered} sin(\beta)\text{ = 0.292} \\ Hypotenuse\text{ = 17.5} \\ Opposite\text{ = ?} \\ Adjacent\text{ = ?} \\ \end{gathered}$

Step 2:

$\begin{gathered} sin\beta\text{ = }\frac{Opposite}{Hypotenuse} \\ 0.292\text{ = }\frac{Opposite}{17.5} \\ Opposite\text{ = 17.5 }\times\text{ 0.292} \\ Opposite\text{ = 5.11} \end{gathered}$

Step 2:

Use the Pythagoras theorem to find the adjacent.

$\begin{gathered} Opposite^2\text{ + Adjacent}^2\text{ = Hypotenuse}^2 \\ 5.11^2\text{ + Adjacent}^2\text{ = 17.5}^2 \\ 26.1121\text{ + Adjacent}^2\text{ = 306.25} \\ Adjacent^2\text{ = 306.25 - 26.1121} \\ Adjacent^2\text{ = 280.1379} \\ Adjacent\text{ = }\sqrt{280.1379} \\ Adjacent\text{ =16.7} \end{gathered}$

Final answer

Adjacent = 16.7 cm