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

Approximated: $9.7$cm
Exact: $12tan(39)$ or $\frac{12}{tan51}$

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:

$tan39 = \frac{x}{12}$ (opposite/adjacent)

Now, isolate the variable, x:
$x = 12tan39$ (exact form)
$x = 9.7$cm (approximated to 1 decimal place)

Answer 2

Answer:

9.7 cm

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