Question

a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length of the hypotenuse if the triangle? round to the nearest tenth.

Answer 1

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

$sin(x) = \frac{opposite\ side}{hypotenuse}$

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

$sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in$

Finally the length of the hypotenuse is 4.1 in