Question

A 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 52 centimeters away from the base of the playground. the slide on the right is positioned at a 30° angle to the ground and is 98 centimeters away from the playground's base. playground with two slides. left slide has base measuring 52 centimeters and base angle of 45 degrees. right slide has base measuring 98 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? 73.5

Answer 1

To find the total length of both slides on the playground, use trigonometry to calculate the length of each slide and then add them together.

Step-by-step explanation:

To find the total length of both slides on the playground, we need to calculate the length of each slide and then add them together.

For the slide on the left, the base is 52 centimeters and the base angle is 45 degrees. We can use trigonometry to find the length of the slide.

The length of the left slide is given by the formula: Length = base / sin(base angle)

Length = 52 / sin(45) = 52 / 0.7071 = 73.638 centimeters (rounded to the nearest tenth).

For the slide on the right, the base is 98 centimeters and the base angle is 30 degrees. Using the same trigonometric formula, we can find the length of the right slide.

Length = 98 / sin(30) = 98 / 0.5 = 196 centimeters (rounded to the nearest tenth).

The total length of both slides is the sum of their lengths: 73.638 + 196 = 269.638 centimeters (rounded to the nearest tenth).

Answer 2

The total length of both slides on the playground is found by calculating the hypotenuse of the right-angled triangles formed by each slide. The length of the left slide is 73.5 cm, and the length of the right slide is 196 cm, giving us a combined total length of 269.5 cm, rounded to the nearest tenth.

Step-by-step explanation:

To determine the total length of both slides on the playground, we need to apply trigonometric functions, specifically the sine function for right-angled triangles. Since we know the angles and base lengths, we can find the hypotenuse, which is the length of each slide.

For the left slide, using the 45° angle, the relationship of the sides in a 45-45-90 triangle is such that the hypotenuse is √2 times the length of each side. Since the base is 52 cm, we have:

Length of left slide = 52 cm × √2 ≈ 52 cm × 1.414 ≈ 73.5 cm

For the right slide, we use the sine function because we know the angle and the opposite side:

sin(30°) = Opposite / Hypotenuse

sin(30°) = 1/2

Hypotenuse = Opposite / sin(30°) = 98 cm / 0.5 = 196 cm

Adding both slide lengths gives us the total length:

Total length = Length of left slide + Length of right slide

Total length = 73.5 cm + 196 cm = 269.5 cm

Rounded to the nearest tenth of a centimeter, the total length of both slides is 269.5 cm.