Question 1103816
your triangle is ABC.


side a is opposite angle A.
side b is opposite angle B.
side c is opposite angle C.


angle C is equal to 90 degrees, therefore side c is the hypotenuse of the right triangle.


the length side a is 8 and the length of side b is 7.


by pythagorus, the square of the hypotenuse is equal to the sum of the square of each leg.


this means that c^2 = a^2 + b^2


since a = 8 and b = 7, then c^2 = 8^2 + 7^2 = 64 + 49 = 113.


take the square root of both sides of that equation to get c = plus or minus square root of 113.


since the length of any side can't be negative, then c = square root of (113).


you are given that angle B is equal to theta.


the side opposite angle B is b.


the side adjacent to angle B that is not the hypotenuse is a.


the tangent of B is equal to opposite / adjacent.


this is equal to side b / side a which is equal to 7/8


the tangent of angle B is equal to 7/8.


since angle B = angle theta, then that's the tangent of angle theta as well.


a diagram of your triangle is shown below:


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