Question

What is the tangent ratio of an obtuse angle 7/25

Answer 1

Explanation:

first of all

tan(x) = sin(x)/cos(x)

that is the tangent ratio.

so, the question is also, what happens to sine and cosine for obtuse angles.

remember the trigonometric triangle inside the circle.

sine is the up/down leg (up = positive, down = negative), cosine is the left/right leg (and extension of the leg; of left from the center = negative, if right from the center = positive).

so, for an obtuse angle (90° < angle <= 180°) sine is still up and therefore positive, but cosine is left from the center and therefore negative.

for that reason tan(angle) = sin(angle)/cos(angle) is negative.

in fact, it is -tan(180 - angle).

Answer 2

Explanation:

In a right-angled triangle, the tangent ratio of an acute angle = the ratio of the length of the opposite side to the length of the adjacent side.

Lets say angle A= 150 degrees (obtuse)

• to find its corresponding acute angle, we need to subtract 150 from 180 degrees, that is, 180-150= 30 degrees.

• Considering a right triangle where angle B=30 degrees. now assuming that the opposite side of angle B has a length of 7 while the adjacent side has a length of 25.

So, the tangent ratio of angle B= the ratio of the length of the opposite side to the length of the adjacent side.

So far we have:

• tan B = opposite/adjacent = 7/25

and because angle A is obtuse, its tangent ratio is the negative of the tangent ratio of its corresponding acute angle.

• So, tan A = -tan 30 = -1/√3 or approximately -0.577.