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For the right triangle shown, use the trig functions to find the value of x. Round your answer to the nearest tenth.

1. 9.1
2. 8.2
3. 9.4
4. 7

For the right triangle shown, use the trig functions to find the value of x. Round your answer to the nearest tenth. 1. 9.1 2. 8.2 3. 9.4 4. 7 class=

Answer :

Sarah06109

Answer:

[tex]\boxed{\boxed {\sf 3. \ 9.4}}[/tex]

Step-by-step explanation:

First, recall the three basic right triangle trigonometry ratios.

  • sin(θ)=opposite/hypotenuse
  • cos(θ)= adjacent/hypotenuse
  • tan(θ)= opposite/adjacent

Theta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.

We are also given 2 sides: 10 and x.

  • 10 is the hypotenuse, because it is opposite the right angle.
  • x is opposite the 70 degree angle.

Since we have the opposite and hypotenuse, we must use sine.

[tex]sin (\Theta)= \frac{opposite}{hypotenuse}}[/tex]

The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.

[tex]sin(70)=\frac{x}{10}[/tex]

We are solving for x. We must isolate x on one side of the equation.

Currently, x is being divided by 10. To "undo" the division, we must perform the inverse operation, which is multiplication. Multiply both sides of the equation by 10.

[tex]10*sin(70)=\frac{x}{10}*10[/tex]

[tex]10*sin(70)=x[/tex]

[tex]10*0.939692621=x[/tex]

[tex]9.39692621=x[/tex]

Round to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.

[tex]9.4 \approx x[/tex]

x is about 9.4

Jessicajackson01

Answer:

First, recall the three basic right triangle trigonometry ratios.

sin(θ)=opposite/hypotenuse

cos(θ)= adjacent/hypotenuse

tan(θ)= opposite/adjacent

Theta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.

We are also given 2 sides: 10 and x.

10 is the hypotenuse, because it is opposite the right angle.

x is opposite the 70 degree angle.

Since we have the opposite and hypotenuse, we must use sine.

sin (\Theta)= \frac{opposite}{hypotenuse}}

The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.

sin(70)=\frac{x}{10}sin(70)=

10

x

We are solving for x. We must isolate x on one side of the equation.

Currently, x is being divided by 10. To "undo" the division, we must perform the inverse operation, which is multiplication. Multiply both sides of the equation by 10.

10*sin(70)=\frac{x}{10}*1010∗sin(70)=

10

x

∗10

10*sin(70)=x10∗sin(70)=x

10*0.939692621=x10∗0.939692621=x

9.39692621=x9.39692621=x

Round to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.

9.4 \approx x9.4≈x

x is about 9.4

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