We are given that the angle a is the right angle. So let us work from this.
ab = 12 (the vertical side of the triangle)
bc = 13 (which if drawn can be clearly observed to be the hypotenuse) = the side opposite to angle a
ca = 5 (the horizontal side of the triangle)
Since we are to find for the cosine ratio of angle c or angle θ, therefore:
cos θ = adjacent side / hypotenuse
cos θ = ca / bc
cos θ = 5 / 13
Check out the attached image below for the illustration of the triangle.
Given:
In a set of 3 numbers the first is a positive integer, the second is 3 more than the first and the 3rd is a square of the second.
To find:
The equation for the given situation if the sum of the numbers is 77.
Solution:
a. Let the first number in the set is x.
The second is 3 more than the first. So, the second number is .
The 3rd number is a square of the second. So, the third number is .
Therefore, the first, second and third numbers are respectively.
b. The sum of the numbers is 77.
First number + Second number + Third number = 77
c. So, the equation in terms of x is:
Therefore, the required equation is .
d. On simplification, we get
Subtract 77 from both sides.
Therefore, the simplified form of the required equation is .