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toddler's playground has two slides on either side. The slide on the left is situated at a 45° angle to the ground and is 64 centimeters away from the base of the playground. The slide on the right is positioned at a 30° angle to the ground and is 106 centimeters away from the playground's base.

Playground with two slides. Left slide has base measuring 64 centimeters and base angle of 45 degrees. Right slide has base measuring 106 centimeters and base angle of 30 degrees.

What is the total length of both slides on this playground, rounded to the nearest tenth of a centimeter?

Toddlers Playground Has Two Slides On Either Side The Slide On The Left Is Situated At A 45 Angle To The Ground And Is 64 Centimeters Away From The Base Of The class=

Sagot :

Macaroni31idn

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

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