Question:
Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.
Solution:
A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:
In this case, the appropriate trigonometric identity is:
[tex]\sin (55^{\circ})\text{ = }\frac{y}{h}[/tex]where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:
[tex]\sin (55^{\circ})\text{ = }\frac{10}{h}[/tex]and solving for h, we get:
[tex]h\text{ = }\frac{10}{\sin (55^{\circ})}\text{ = 12.207}\approx12.21[/tex]then, the correct answer is:
[tex]h\text{ =}12.21[/tex]
