Answer :

Answer:

(a) height ≈ 1.9 m (b) length of slide ≈ 3.0 m

Step-by-step explanation:

(a)

To calculate the height of the slide

Using the sine ratio on the right triangle on the left

let height be h , then

sin70° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{2}[/tex] ( multiply both sides by 2 )

2 × sin70° = h , then

h ≈ 1.9

That is the height of the slide h ≈ 1.9 m

(b)

To calculate the length of the slide

Using the sine ratio on the right triangle on the right

let s be the length of the slide, then

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{s}[/tex] ≈ [tex]\frac{1.9}{s}[/tex] ( multiply both sides by s )

s × sin40° ≈ 1.9 ( divide both sides by sin40° )

s ≈ [tex]\frac{1.9}{sin40}[/tex] ≈ 3.0

That is the length of the slide s ≈ 3.0 m

tessyaelv
Answer:

a) Height of the slide = 1.5 m
b) The length of the slide = 1.1 meters

a) We’ll use the function sine, which uses the *opposite side* and *hypotenuse* to find the height, because the dotted line forms 2 right triangle, where trigonometric functions can be applied. The height of the slide will be represented by x.

sin (70°) = x/2.

Multiply by 2 on both sides to isolate x and find its value.

sin (70°)*2 = x

Run this through a calculator, and x = 1.5478.
The question says to round the nearest tenth. 4<5, so round down to x = 1.5 meters.

b) The slide is the hypotenuse of the second right triangle formed by the altitude, which we now have the measure of and can use to find the measure of the slide. The height of the biggest triangle is opposite the angle 40° that we will be using. We will use sine again since we are working with the opposite side and the hypotenuse. The slide’s measure = y.

sin(40°) = 1.5/y

Multiply by y on both sides to get it out of the denominator.

sin(40°)*y = 1.5

Multiply sin(40°) on both sides to isolate y.

y = sin(40°)*1.5

Put sin(40°)*1.5 into a calculator, and y = 1.117
We have to round to the nearest tenth, and the 1 that is in the hundredth place is <5, so round down to y = 1.1 meters.

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