Since the sum of the squares of the two shortest sides is equal to the square of the longest side, this triangle is right. Now let's recall the definition of tangent.
If△ ABCis a right triangle with acute∠ A,
then the tangent of∠ Ais the ratio of the length of the leg opposite∠ A to the length of the leg adjacent∠ A.
Having this definition in mind, we will make a picture and name the vertices. The right angle will be located opposite the longest side.
Notice that in this triangle the greater acute angle lies opposite the longer leg. Therefore, we need to find the tangent of ∠ B. Now we will write an appropriate ratio using the definition we recalled.
tan B=4/3≈ 1.33
The tangent of the greater angle in this triangle is 43 or approximately 1.33.
