Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4
2 answers:
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Approximated: 
cm
Exact:
or 
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:
(opposite/adjacent)
Now, isolate the variable, x:
(exact form)
cm (approximated to 1 decimal place)
Exact:
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:
Now, isolate the variable, x: