SOLUTION: use the Pythagorean theorem to find the length of the missing side. then find the indicated trigonometric function of the given angle. give an exact answer with a rational denomina

Algebra ->  Trigonometry-basics -> SOLUTION: use the Pythagorean theorem to find the length of the missing side. then find the indicated trigonometric function of the given angle. give an exact answer with a rational denomina      Log On


   

Question 1103816: use the Pythagorean theorem to find the length of the missing side. then find the indicated trigonometric function of the given angle. give an exact answer with a rational denominator. find tan theta.
C=90 degrees B=theta a=8 b=7
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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:

$$$