A ramp has a height of 5.8 feet and an angle of 80°. A sketch of the ramp is shown.
What is the length of the ramp, y, to the nearest tenth of a foot?
To find the length of the ramp, we can use the trigonometric function sine.
In this case, we need to find the length opposite to the given angle, which is the height of the ramp.
We can set up the equation sin(80°) = 5.8/y, where y is the length of the ramp we want to find.
Using the property of sine, we can rewrite the equation as sin(80°) = 5.8/y.
Solving for y, we have y = 5.8/sin(80°).
Using a calculator, sin(80°) ≈ 0.9848.
Substituting this value into the equation, we have:
y = 5.8/0.9848 ≈ 5.88 feet.
Therefore, the length of the ramp, y, is approximately 5.9 feet to the nearest tenth.
To find the length of the ramp (y), we can use the concept of trigonometry. Since we know the height of the ramp (5.8 feet) and the angle (80°), we can use the trigonometric function of sine.
The sine function relates the opposite side (height) and the hypotenuse (length of the ramp) of a right triangle:
sin(angle) = opposite / hypotenuse
In this case, the opposite side is the height (5.8 feet), so we can rewrite the equation as:
sin(80°) = 5.8 / y
To solve for y, we can rearrange the equation:
y = 5.8 / sin(80°)
Using a calculator, we can evaluate sin(80°) to be approximately 0.9848. Substituting this value into the equation, we get:
y = 5.8 / 0.9848
Calculating this, we find:
y ≈ 5.892 feet
Rounding to the nearest tenth of a foot, the length of the ramp (y) is approximately 5.9 feet.