Answer:
The combined slide length is about 212.9 centimeter.
Step-by-step explanation:
The bottom of the slides are right angles, with the slides acting as the hypotenuse. Let's use trigonometry to find the length of the slides.
Remember SOH CAH TOA, which helps us remember which trigonomic functions should be used to find the side lengths of a right triangle. In these triangles, we know the angle measure of one angle and the length of its adjacent side, and we are trying to find the length of the hypotenuse. So we should use the cosine function.
We know that [tex]\cos( \theta) = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]. Since we know the value of θ and the adjecent side for both triangles, we can find the length of their hypotenuses.
Let's start with the shorter slide.
[tex]\cos(45)=\frac{64}{h} \\\frac{\sqrt{2}}{2}=\frac{64}{h}\\h*\frac{\sqrt{2}}{2}=64\\h = \frac{128}{\sqrt{2}}[/tex]
Now let's do the longer slide.
[tex]\cos(30)= \frac{106}{h}\\\frac{\sqrt{3}}{2}=\frac{106}{h}\\\sqrt{3}*h=212\\h=\frac{212}{\sqrt{3}}[/tex]
The last step is the add the two slide lengths.
128/√2 + 212/√3 ≈ 212.9
