Question:
In which triangle is the measure of the unknown angle, x, equal to the value of [tex]sin^{-1}(\frac{5}{8.3})?[/tex]
- A right triangle is shown. The length of the hypotenuse is 8.3 and the length of another side is 5. Angle x is between those sides.
- A right triangle is shown. The length of the hypotenuse is 8.3 and the length of another side is 5. Angle x is opposite to side with length 5.
- A right triangle is shown. The length of the hypotenuse is 5 and the length of another side is 8.3. The angle opposite to side with length 8.3 is x.
- A right triangle is shown. The length of 2 sides are 8.3 and 5. The angle opposite to side with length 5 is x.
Answer:
The length of the hypotenuse is 8.3 and the length of another side is 5. Angle x is opposite to side with length 5.
Step-by-step explanation:
Given
[tex]x = sin^{-1}(\frac{5}{8.3})[/tex]
Required
Determine the triangle that illustrates the given parameters
From the list of given options, we understand the the triangle is a right angled triangle.
Provided that
[tex]x = sin^{-1}(\frac{5}{8.3})[/tex]
Take sin of both sides
[tex]sin\ x = sin(sin^{-1}(\frac{5}{8.3}))[/tex]
[tex]sin\ x = \frac{5}{8.3}[/tex]
From trigonometry; we understand that
[tex]sin\ x = \frac{Opp}{Hyp}[/tex]
Where Opp is the Opposite and Hyp is the Hypotenuse of the triangle
By comparison, this means that
[tex]Opp = 5\\Hyp = 8.3[/tex]
From the list of given options;
The option that best fit the illustration above is option B;
Because of the following;
1. The length of the hypotenuse is 8.3
2. The length of another side is 5.
3. Angle x is opposite to side with length 5.
See attachment for the actual triangle;
