Question

a ramp 40 ft long rises to a platform. the bottom of the platform is 17 ft from the foot of the ramp. find x, the answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the hypotenuse of the triangle is the length of the ramp ($c = 40$ ft) and the adjacent side to the angle $x$ is the distance from the foot of the ramp to the bottom of the platform ($a=17$ ft). We use the cosine function $\cos(x)=\frac{a}{c}$.

Step2: Calculate the cosine value

Substitute $a = 17$ and $c = 40$ into the cosine formula: $\cos(x)=\frac{17}{40}=0.425$.

Step3: Find the angle

To find the angle $x$, we take the inverse cosine of 0.425. So $x=\cos^{-1}(0.425)$. Using a calculator, $x\approx64.9^{\circ}$. Rounding to the nearest tenth of a degree, $x\approx64.9^{\circ}\approx64.0^{\circ}$.

Answer:

$x = 64.0^{\circ}$