Question

draw a right triangle with a leg that as a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to nearest tenth.

Answer 1

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:

`\sin (55^(\circ))\text{ = }(y)/(h)`

where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:

`\sin (55^(\circ))\text{ = }(10)/(h)`

and solving for h, we get:

`h\text{ = }(10)/(\sin (55^(\circ)))\text{ = 12.207}\approx12.21`

then, the correct answer is:

`h\text{ =}12.21`