Question

in a right triangle, if angle O is equal to 39 and the side adjacent to is equal to 12.0 centimeters, what is the approximate length of the opposite side?

Answer 1

9.7 cm

Step-by-step explanation: I took the test.

Answer 2

Approximated:
`9.7`cm
Exact:
`12tan(39)` or
`(12)/(tan51)`

Step-by-step explanation:
It's always best for these types of questions to visualise it. A right triangle has base angle of 90°. Mark in what you know, and leave out the rest. Notice how the question doesn't ask for a hypotenuse. This means that you might be using the tangent function as the tangent function also doesn't require a hypotenuse.

So now, you have a side of 12cm, with the corresponding 39° angle marked.
To find the missing length, you can use the tangent function to approximate the length:


`tan39 = (x)/(12)` (opposite/adjacent)

Now, isolate the variable, x:

`x = 12tan39` (exact form)

`x = 9.7`cm (approximated to 1 decimal place)