Math / Geometry

Question4. The diagram shows a sketch of the cross section of an access ramp. What is the measure of the indicated angle in degrees?

Studdy Solution

STEP 1

What is this asking? We need to find the angle of elevation of a ramp that's 5 meters long and 2 meters high. Watch out! Make sure your calculator is in degree mode, not radians!
Also, don't mix up the sides of the triangle when using trigonometric functions.

STEP 2

1. Set up the trigonometric ratio.
2. Calculate the angle.

STEP 3

Alright, let's do this!
We've got a right triangle here, so we can use our trigonometric friends – sine, cosine, and tangent.
We know the opposite side ( $2$ meters) and the adjacent side ( $5$ meters) to the angle we're looking for.

STEP 4

Which trig function uses opposite and adjacent?
That's our pal tangent!
Remember: tangent is opposite over adjacent!
So, we can write: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

STEP 5

Let's plug in our values: $\tan(\theta) = \frac{2}{5}$ Awesome! We've set up our equation.
Now, let's solve for that angle!

STEP 6

To find the angle $\theta$ , we need to use the inverse tangent (also called arctangent, denoted as $\arctan$ or $\tan^{-1}$ ).
This function basically "undoes" the tangent, giving us the angle whose tangent is $2/5$ .

STEP 7

So, we have: $\theta = \arctan\left(\frac{2}{5}\right)$

STEP 8

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers!
You should get: $\theta \approx 21.80^\circ$ Boom! We found our angle!

STEP 9

The angle of elevation of the ramp is approximately $21.80^\circ$ .

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Question4. The diagram shows a sketch of the cross section of an access ramp. What is the measure of the indicated angle in degrees?

Studdy Solution

STEP 1

What is this asking? We need to find the angle of elevation of a ramp that's 5 meters long and 2 meters high. Watch out! Make sure your calculator is in degree mode, not radians!
Also, don't mix up the sides of the triangle when using trigonometric functions.

STEP 2

1. Set up the trigonometric ratio.
2. Calculate the angle.

STEP 3

Alright, let's do this!
We've got a right triangle here, so we can use our trigonometric friends – sine, cosine, and tangent.
We know the opposite side ( $2$ meters) and the adjacent side ( $5$ meters) to the angle we're looking for.

STEP 4

Which trig function uses opposite and adjacent?
That's our pal tangent!
Remember: tangent is opposite over adjacent!
So, we can write: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

STEP 5

Let's plug in our values: $\tan(\theta) = \frac{2}{5}$ Awesome! We've set up our equation.
Now, let's solve for that angle!

STEP 6

To find the angle $\theta$ , we need to use the inverse tangent (also called arctangent, denoted as $\arctan$ or $\tan^{-1}$ ).
This function basically "undoes" the tangent, giving us the angle whose tangent is $2/5$ .

STEP 7

So, we have: $\theta = \arctan\left(\frac{2}{5}\right)$

STEP 8

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers!
You should get: $\theta \approx 21.80^\circ$ Boom! We found our angle!

STEP 9

The angle of elevation of the ramp is approximately $21.80^\circ$ .

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Question4. The diagram shows a sketch of the cross section of an access ramp. What is the measure of the indicated angle in degrees?

Studdy Solution

STEP 1

What is this asking? We need to find the angle of elevation of a ramp that's 5 meters long and 2 meters high. Watch out! Make sure your calculator is in degree mode, not radians!Also, don't mix up the sides of the triangle when using trigonometric functions.

STEP 2

1. Set up the trigonometric ratio.2. Calculate the angle.

STEP 3

Alright, let's do this!We've got a right triangle here, so we can use our trigonometric friends – sine, cosine, and tangent.We know the **opposite side** (222 meters) and the **adjacent side** (555 meters) to the angle we're looking for.

STEP 4

Which trig function uses opposite and adjacent?That's our pal **tangent**!Remember: tangent is opposite over adjacent!So, we can write: tan⁡(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite​

STEP 5

Let's plug in our **values**: tan⁡(θ)=25\tan(\theta) = \frac{2}{5}tan(θ)=52​ Awesome! We've set up our equation.Now, let's solve for that angle!

STEP 6

To find the angle θ\thetaθ, we need to use the **inverse tangent** (also called arctangent, denoted as arctan⁡\arctanarctan or tan⁡−1\tan^{-1}tan−1).This function basically "undoes" the tangent, giving us the angle whose tangent is 2/52/52/5.

STEP 7

So, we have: θ=arctan⁡(25)\theta = \arctan\left(\frac{2}{5}\right)θ=arctan(52​)

STEP 8

Now, grab your calculator, make sure it's in **degree mode**, and punch in those numbers!You should get: θ≈21.80∘\theta \approx 21.80^\circθ≈21.80∘ Boom! We found our angle!

STEP 9

The angle of elevation of the ramp is approximately 21.80∘21.80^\circ21.80∘.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the angle of elevation of a ramp that's 5 meters long and 2 meters high. Watch out! Make sure your calculator is in degree mode, not radians!
Also, don't mix up the sides of the triangle when using trigonometric functions.

1. Set up the trigonometric ratio.
2. Calculate the angle.

Alright, let's do this!
We've got a right triangle here, so we can use our trigonometric friends – sine, cosine, and tangent.
We know the opposite side ( $2$ meters) and the adjacent side ( $5$ meters) to the angle we're looking for.

Which trig function uses opposite and adjacent?
That's our pal tangent!
Remember: tangent is opposite over adjacent!
So, we can write: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Let's plug in our values: $\tan(\theta) = \frac{2}{5}$ Awesome! We've set up our equation.
Now, let's solve for that angle!

To find the angle $\theta$ , we need to use the inverse tangent (also called arctangent, denoted as $\arctan$ or $\tan^{-1}$ ).
This function basically "undoes" the tangent, giving us the angle whose tangent is $2/5$ .

So, we have: $\theta = \arctan\left(\frac{2}{5}\right)$

Now, grab your calculator, make sure it's in degree mode, and punch in those numbers!
You should get: $\theta \approx 21.80^\circ$ Boom! We found our angle!

The angle of elevation of the ramp is approximately $21.80^\circ$ .