I need help badly, ok I have a right angle ramp and it is going off the uniform federal accessibility standers. It states that the ramp angle used for a wheelchair ramp must be less than or equal to 4.78 and all ramps are created to be right triangles.
Ok the 2nd question is : if the ramp angle is 4. 75 degrees, determine the measure of the third angle of the triangle
To find the measure of the third angle of the triangle, we first need to find the measure of the other angle in the triangle.
Since the ramp angle is 4.75 degrees, we know that it is one of the acute angles of the triangle. The third angle of a triangle is always the right angle, which is 90 degrees.
To find the measure of the third angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we can subtract the measures of the two known angles from 180 degrees to find the measure of the third angle:
90 degrees (right angle) + 4.75 degrees = 94.75 degrees
180 degrees - 90 degrees - 4.75 degrees = 85.25 degrees
Therefore, the measure of the third angle of the triangle is 85.25 degrees.
Ok here is the 3rd question and thanks for the help on the 2nd
: To meet the uniform federal accessibility standards, which side will be the shortest side of the triangle?
To determine which side of the triangle will be the shortest side, we need to consider the trigonometric ratios involving the angles of the triangle.
In a right triangle, the side opposite the smallest angle is the shortest side. Since the ramp angle is 4.75 degrees, this is the smallest angle in the triangle.
In a right triangle, the side opposite the smallest angle is the side opposite the acute angle, which is the smallest side. Therefore, the shortest side of the triangle will be the side opposite the 4.75-degree angle.
To calculate the shortest side, you can use trigonometric ratios such as sine, cosine, or tangent. Since we are given the angle and the angle is the smallest, the side opposite the angle can be easily calculated using the sine ratio:
sin(4.75 degrees) = Length of shortest side / Hypotenuse
Hypotenuse is the longest side of the triangle, which is opposite the right angle and can be considered the ramp length in this case.
Therefore, the side opposite the 4.75-degree angle will be the shortest side of the triangle.
Ok thanks a lot! Here is the last question: The length of a ramp is 3 feet long and its vertical rise is 20 inch. Explain why it is or is not possible to have a horizontal distance of 16 inch
To determine if it is possible to have a horizontal distance of 16 inches for the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Given that the ramp length is 3 feet (which is 36 inches) and the vertical rise is 20 inches, we can consider the ramp as a right triangle where the hypotenuse (ramp length) is 36 inches, one side is the vertical rise of 20 inches, and the other side could be the horizontal distance we want to determine if it is possible.
Let's assume the horizontal distance is 16 inches. Using the Pythagorean theorem:
(16)^2 + (20)^2 = (36)^2
256 + 400 = 1296
656 = 1296
This shows that for a horizontal distance of 16 inches, the lengths of the sides do not satisfy the Pythagorean theorem within the given ramp length of 3 feet (36 inches) and vertical rise of 20 inches. Therefore, it is not possible to have a horizontal distance of 16 inches within these constraints.