Answer:
tan(29°) = Opposite side / 4
Now, solve for the opposite side:
Opposite side = 4 * tan(29°)
Using a calculator:
Opposite side ≈ 4 * 0.5543 ≈ 2.2172
Explanation:
You have a triangle with an angle of 29° and one side length of 4 units. You want to find the length of the side opposite the 29° angle, which we'll call "x" and it's inside the green box.
We'll use the tangent (tan) trigonometric function, which is defined as:
tan(angle) = Opposite side / Adjacent side
In your case, the angle is 29°, the opposite side is "x" (what we're trying to find), and the adjacent side is 4 (given in the problem).
Write down the equation using the tangent function:
tan(29°) = x / 4
- Now, you need to solve for "x." To do this, first find the value of tan(29°) using a calculator.
tan(29°) ≈ 0.5543 (rounded to four decimal places)
- Now, rewrite the equation with the value of tan(29°):
0.5543 = x / 4
- To isolate "x," multiply both sides of the equation by 4:
0.5543 * 4 = x
Calculate the result:
x ≈ 2.2172
- Finally, round the answer to the nearest hundredth (two decimal places):
x ≈ 2.22
So, the number that belongs in the green box is approximately 2.22 units.