Algebra-2

Let's assume that the triangle has a right angle at vertex A, and side AB is the horizontal side adjacent to angle 𝜃, and side BC is the vertical side opposite to angle 𝜃.

 

Given that cos 𝜃 = , we know that the adjacent side AB is 7 units and the hypotenuse AC is 8 units.

 

Using the Pythagorean theorem, we can calculate the length of side BC (the opposite side):

 

BC² = AC² - AB²

BC² = 8² - 7²

BC² = 64 - 49

BC² = 15

BC = √15

 

Now, we have the lengths of all three sides of the right triangle: AB = 7, BC = √15, and AC = 8.

 

Since we're interested in finding the value of tan 𝜃, which is the ratio of the opposite side to the adjacent side, we have:

 

tan 𝜃 =