The questions are illustrations of Pythagoras theorem and trigonometry ratios.
<h3>What is Pythagoras theorem?</h3>
Pythagoras theorem is used to determine the lengths of the legs of a right triangle.
It is represented as:
Where:
b & c are the legs of the triangle, while a is the hypotenuse
<u>Question 16</u>
Start by calculating the value of x, using the sine ratio
Evaluate sin(30)
Solve for x
Next, calculate the length (l) of the boundary between both triangles using Pythagoras theorem
Collect like terms
Take the square root of both sides
Given that the angle is 45 degrees, it means that:
So, we have:
Divide through by 2
Take the square root of both sides
Hence, the values of x, y and z are:
<u>Question 18</u>
Start by calculating the value of z, using the sine ratio
Evaluate sin(45)
Solve for z
Next, calculate the value of y using tangent ratio
Solve for y
Evaluate tan(30)
Next, calculate the value of x using sine ratio
Solve for x
Evaluate sin(30)
Hence, the values of x, y and z are:
<u>Question 20</u>
Start by calculating the value of z, using the sine ratio
Evaluate sin(45)
Solve for z
Simplify
Next, calculate the value of y using tangent ratio
Solve for y
Evaluate tan(30)
Simplify
Next, calculate the value of x using sine ratio
Solve for x
Evaluate sin(30)
Hence, the values of x, y and z are:
Read more about Pythagoras theorem and trigonometry ratios at:
brainly.com/question/6241673