A ranger spots a forest fire while on a 45-meter observation tower. The angle of depression from the tower to the fire is 12 degrees. To the nearest meter, how far is the fire from the base of the tower?

IS THE ANSWER 212 meters

For Texas Connections Academy- ALG 1B:Q Unit 6: Radical Expressions and Equations (Lesson 6: Trigonometric Ratios):

1. C
2. D
3. C
4. B
5. A
6. A
7. D
8. B
9. A
I am aware answers change from time to time; these are the answers in the 2018-19 school year. These may not be the same answers some time from now.

(P.S. Last day of school 2018- 2019 school year!!!) ^.^

still right in 2022 :D happy last day of algebra guys

FINALLY I FOUND SOMEONE WHO ACTUALLY GAVE OUT ALL THE ANSWERS-

thanks for the help "posted by," it was terribly needed, I got 100%

Answers?!

Thank you posted by!!! Savior!

You're welcome! I'm glad I could help. Don't hesitate to ask if you need further assistance or have any other questions.

To find the distance from the base of the tower to the fire, we can use trigonometry. Specifically, we can use the tangent function.

First, let's draw a diagram to visualize the situation. Let "A" represent the top of the tower, "B" represent the base of the tower, and "C" represent the location of the fire. The angle of depression is the angle formed between the horizontal line AB and the line AC, which is the line of sight from the ranger to the fire.

We know that the angle of depression is 12 degrees. We also know that the height of the tower AB is 45 meters.

Using a trigonometric ratio, we can write:

tangent(angle of depression) = opposite / adjacent

In this case, the opposite side is AB (45 meters) and the adjacent side is BC, which is the distance from the base of the tower to the fire.

So we have:

tangent(12 degrees) = 45 meters / BC

Now we can solve for BC:

BC = 45 meters / tangent(12 degrees)

Using a calculator, the tangent of 12 degrees is approximately 0.212557. Dividing 45 meters by this value, we get approximately 211.9249 meters.

Rounding this value to the nearest meter, we find that the fire is approximately 212 meters from the base of the tower.

Therefore, the answer is indeed 212 meters.

5.5m rounded to the nearest tenth

54/d= tan12

d= 54/tan12