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3 years ago

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

Mathematics

2 answers:

jeka57 [31]3 years ago

7 0

Answer:

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

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 <u>hypotenuse</u>, because it is opposite the right angle.
x is <u>opposite </u>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.

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

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.

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

$10*sin(70)=x$

$10*0.939692621=x$

$9.39692621=x$

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 <u>9.4</u>

Alecsey [184]3 years ago

3 0

Answer:

<h3>First, recall the three basic right triangle trigonometry ratios.</h3>

<h3>sin(θ)=opposite/hypotenuse</h3><h3>cos(θ)= adjacent/hypotenuse</h3><h3>tan(θ)= opposite/adjacent</h3><h3>Theta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.</h3>

<h3>We are also given 2 sides: 10 and x.</h3>

<h3>10 is the hypotenuse, because it is opposite the right angle.</h3><h3>x is opposite the 70 degree angle.</h3><h3>Since we have the opposite and hypotenuse, we must use sine.</h3>

<h3>sin (\Theta)= \frac{opposite}{hypotenuse}}</h3>

<h3>The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.</h3>

<h3>We are solving for x. We must isolate x on one side of the equation.</h3>

<h3>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.</h3>

<h3>Round to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.</h3>

<h3>9.4 \approx x9.4≈x</h3>

<h3>x is about 9.4</h3>

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PLEASE ANSWER ASAP For the equation y=2x2-16x+30 Identify the vertex and convert into vertex form. STEP BY STEP PLEASE EXPLAIN H

Mnenie [13.5K]

Answer:

Step-by-step explanation:

To put a quadratic into vertex form, you need to complete the square on it. Do this by following these steps. I'll tell you what we're doing and then show you what it looks like.

First step is to set the quadratic equal to 0 and then move the constant over. That's 2 steps in one, but not confusing at all. That looks like this:

$2x^2-16x=-30$

Next, the rule is that the leading coefficient has to be a positive 1. Ours is a 2, so we will factor out a 2 but only from the left side. That looks like this:

$2(x^2-8x)=-30$

Next step is to take half the linear term (the number with the x attached to it, not the x-squared), square it, and add it in to both sides. This is where things get a bit tricky, so pay attention. Our linear term is 8, half of 8 is 4, and 4 squared is 16. So we add 16 in. We'll do it to the left only first:

$2(x^2-8x+16)$

That's the left side. Notice that there is still a 2 out front there. That 2 is a multiplier. That means that what we actually added in was 2(16) = 32, not just 16. Now adding that to the right makes the whole thing:

$2(x^2-8x+16)=-30+32$

Completing the square allows us to create a perfect square binomial on the left which is in the form (x - )². That blank space is filled in with the number we squared and then added in. We squared a 4 to get 16, so our perfect square binomial is (x - 4)². Putting that together:

$2(x-4)^2=2$