In which triangle is the measure of the unknown angle, [tex]$x$[/tex], equal to the value of [tex]$\sin ^{-1}\left(\frac{5}{8.3}\right) ?$[/tex]
Answer (2)
The triangle where the angle x equals sin − 1 ( 8.3 5 ) is a right triangle with an opposite side of length 5 and a hypotenuse of length 8.3. To verify, the sine of angle x equals the ratio of these lengths. Thus, x = sin − 1 ( 8.3 5 ) represents the desired angle in the triangle.
;
The problem requires finding a triangle where the sine of an angle x is equal to 8.3 5 .
This means we are looking for a right triangle where the ratio of the opposite side to the hypotenuse is 8.3 5 .
We need to identify a right triangle with opposite side 5 and hypotenuse 8.3.
The triangle must satisfy the condition sin ( x ) = 8.3 5 , so x = sin − 1 ( 8.3 5 ) .
Explanation
Problem Analysis The problem states that we need to find a triangle where the unknown angle x satisfies the equation x = sin − 1 ( 8.3 5 ) . This means that sin ( x ) = 8.3 5 . In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we are looking for a right triangle where the ratio of the opposite side to the hypotenuse is 8.3 5 .
Solution Plan We need to examine the given triangles and check if any of them are right triangles. For each right triangle, we need to identify the side opposite to the angle x and the hypotenuse. Then, we need to calculate the ratio of the opposite side to the hypotenuse and see if it is equal to 8.3 5 .
Identifying the Triangle Let's assume we have a right triangle with an angle x , where the side opposite to x has length 5 and the hypotenuse has length 8.3. Then, sin ( x ) = 8.3 5 . Therefore, the triangle we are looking for is a right triangle where the side opposite to the angle x is 5 and the hypotenuse is 8.3.
Final Answer Without the image of the triangles, I can't definitively identify which triangle has the specified properties. However, the triangle we are looking for must be a right triangle where the ratio of the side opposite to angle x to the hypotenuse is 8.3 5 .
Examples
Imagine you're building a ramp for skateboarding. You want the ramp to have an angle x such that the sine of the angle is 8.3 5 . This means that for every 8.3 meters of ramp length (the hypotenuse), the ramp rises 5 meters in height (the opposite side). This ensures the ramp has the desired steepness for a smooth ride.
