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

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

probability for j is 1/4

while

a is 1/6