Answer:
6. x° is approximately 21.04°
7. x° is approximately 39.56°
8. x° is approximately 58.03°
9. x° is approximately 72.85°
Step-by-step explanation:
6. In the given right triangle (a triangle with the measure of one of the interior angles equal to 90°, indicated by the small square between two sides) , we have;
The hypotenuse side length = 15
The adjacent side to the given reference angle, x° = 14
By trigonometric ratio, we have;
[tex]cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}[/tex]
[tex]\therefore cos(x^{\circ}) = \dfrac{14}{15}[/tex]
To find the value of x°, we make use of the inverse cosine function, arccos found on a scientific calculator, as follows;
x° = arccos(14/15) ≈ 21.04°
x° ≈ 21.04°
7. In the given right triangle, we have;
The length of the opposite side to the given reference angle, x° = 19
The length of the adjacent side to the given reference angle, x° = 23
By trigonometric ratios, we have;
[tex]Tan(\angle X) = \dfrac{Opposite \, side \ length}{Adjacent\, side \ length}[/tex]
[tex]\therefore tan(x^{\circ}) = \dfrac{19}{23}[/tex]
Therefore;
x° = arctan(19/23) ≈ 39.56°
x° ≈ 39.56°
8. In the given right triangle, the adjacent side to the reference angle, x° and the hypotenuse side are given, therefore, we have;
x° = arccos(9/17) ≈ 58.03°
x° ≈ 58.03°
9. The opposite side to the reference angle and the hypotenuse side are given
By trigonometric ratio, we have;
[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
[tex]\therefore sin(x^{\circ}) = \dfrac{43}{45}[/tex]
x° = arcsin(43/45) ≈ 72.85°
x° ≈ 72.85°.
