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A slide is 4.1 m long and makes an angle with the ground of 40 ° . To the nearest hundredth of a meter, how far above the ground is the top of the slide? Please show all work. Thanks!

A slide is 41 m long and makes an angle with the ground of 40 To the nearest hundredth of a meter how far above the ground is the top of the slide Please show a class=

Respuesta :

Answer:

x ≈ 2.64 m

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4.1}[/tex] ( multiply both sides by 4.1 )

4.1 × sin40° = x , then

x ≈ 2.64 m ( to the nearest hundredth )

The top of the slide is 2.64 m above the ground

semsee45

Answer:

2.64 m

Step-by-step explanation:

The given diagram shows a right triangle with a hypotenuse measuring 4.1 m and an angle of 40° between the hypotenuse and the base of the triangle. To find the measure of the side opposite the angle, we can use the sine trigonometric ratio:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]

In this case:

  • θ = 40°
  • O = x
  • H = 4.1 m

Substitute these values into the sine ratio:

[tex]\sin 40^{\circ}=\dfrac{x}{4.1}[/tex]

Solve for x:

[tex]x=4.1 \sin 40^{\circ}\\\\x=2.6354291997...\\\\x=2.64\; \sf m[/tex]

Therefore, the value of x is:

[tex]\Large\boxed{\boxed{x=2.64\; \sf m}}[/tex]

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