Answer:
x = 4
y = 6
Step-by-step explanation:
Given:
An angle is 45°
The length of the opposite side, hypotenuse and adjacent side of the right triangle is 4, y and x.
Find x, y.
Solution:
In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.
[tex]tan\theta = \frac{Opposite\ side}{Adjacent\ side}[/tex]
[tex]tan(45) = \frac{4}{x}[/tex]
[tex]x = \frac{4}{tan(45)}[/tex]
Now we substitute tan(45) = 1 in above equation.
[tex]x = \frac{4}{1}[/tex]
x = 4
The adjacent side of the right triangle is 4.
Now, we use Pythagoras theorem for determine y value.
[tex]c^{2}=a^{2} + b^{2}[/tex]---------(1)
where c = hypotenuse of triangle.
a = Adjacent side
b = Opposite side
Now, we substitute value of adjacent side and opposite side in equation 1.
[tex]y^{2}=4^{2} + 4^{2}[/tex]
[tex]y^{2}=16 + 16[/tex]
[tex]y^{2}=36[/tex]
y = 6
Therefore, the value x = 4 and y = 6.
