How to find positive tangent - ACT Math
Card 0 of 4
For triangle 
, what is the cotangent of angle 
?
For triangle
The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is 
The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is
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What is the tangent of the angle formed between the origin and the point 
if that angle is formed with one side of the angle beginning on the 
-axis and then rotating counter-clockwise to ? Round to the nearest hundredth.
What is the tangent of the angle formed between the origin and the point
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the 
-axis as your reference point for your angle. (Hence, it is called the "reference angle.")
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
or, for your data, 
, or 
. Since 
is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
Compare your answer with the correct one above
What is the tangent of the angle formed between the origin and the point 
if that angle is formed with one side of the angle beginning on the 
-axis and then rotating counter-clockwise to ? Round to the nearest hundredth.
What is the tangent of the angle formed between the origin and the point
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the 
-axis as your reference point for your angle. (Hence, it is called the "reference angle.")
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
or, for your data, 
.
This is 
. Rounding, this is 
. Since 
is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
This is
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A ramp is being built at an angle of 
from the ground. It must cover 
horizontal feet. What is the length of the ramp? Round to the nearest hundredth of a foot.
A ramp is being built at an angle of
Based on our information, we can draw this little triangle:
Since we know that the tangent of an angle is 
, we can say:
This can be solved using your calculator:
or 
Now, to solve for 
, use the Pythagorean Theorem, 
, where 
and 
are the legs of a triangle and 
is the triangle's hypotenuse. Here, 
, so we can substitute that in and rearrange the equation to solve for 
:
Substituting in the known values:
, or approximately 
. Rounding, this is 
.
Based on our information, we can draw this little triangle:
Since we know that the tangent of an angle is
This can be solved using your calculator:
Now, to solve for
Substituting in the known values:
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