For the right triangle shown, what is the tangent of angle a?
a) 2/3
b) 3/2
c) 3/4
d) 4/3

The correct answer is option C   3/4

Step-by-step explanation:

It is given a right angled triangle ABC

To find the value of x

Hypotenuse² = Base² + height²

(x + 2)² = x² + (x + 1)²

x² + 4x + 4 = x² + x² + 2x + 1

x² -2x -3 = 0

We get x = 3 and x = -1

We take positive value x = 3

To find Tan A

Tan A = Opposite side/Adjacent side

 = BC/AB = x/(x + 1) = 3/4

Therefore the correct answer is option C.   3/4

(x+3)(x+7)

step-by-step explanation:

4+4+2x

or

2x+8

step-by-step explanation: