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Math  /  Trigonometry

Questionslove for aictace ond ongle os elvatian

Studdy Solution

STEP 1

What is this asking? How far is the truck from the bridge, given its height and the angle of elevation? Watch out! Make sure your calculator is in degree mode, not radians!

STEP 2

1. Set up the problem
2. Calculate the distance

STEP 3

We've got a **right triangle** here!
The bridge is the **opposite side**, the distance to the truck is the **adjacent side**, and we're given the **angle** between the adjacent side and the hypotenuse.

STEP 4

Which trig function relates the opposite and adjacent sides?
It's **tangent**!
Remember: tan⁡(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}.

STEP 5

We know the **angle** (θ=39∘\theta = 39^\circ) and the **opposite side** (800800m).
Let's call the **adjacent side** 'xx' (that's what we're trying to find!). So, we have tan⁡(39∘)=800x\tan(39^\circ) = \frac{800}{x}.

STEP 6

To get *x* by itself, we can multiply both sides of the equation by *x* and then divide both sides by tan⁡(39∘)\tan(39^\circ).
This gives us x=800tan⁡(39∘)x = \frac{800}{\tan(39^\circ)}.

STEP 7

Now, grab your calculator (make sure it's in degree mode!) and calculate: x=800tan⁡(39∘)≈8000.80978≈988.05x = \frac{800}{\tan(39^\circ)} \approx \frac{800}{0.80978} \approx 988.05.

STEP 8

The truck is approximately **988.05 meters** away from the bridge.

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