Question

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

Answer 1

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

Answer 2

`\boxed{\boxed {\sf 3. \ 9.4}}`

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.

`sin (\Theta)= (opposite)/(hypotenuse)}`

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

`sin(70)=(x)/(10)`

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)=(x)/(10)*10`

`10*sin(70)=x`

`10*0.939692621=x`

`9.39692621=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 x`

x is about 9.4