$MathMaster logo$

MathMaster

Home
general
a forest ranger sights a fire to the south a second ranger 8 miles east of the first ranger also sights the fire the beari

Question

A forest ranger sights a fire to the South. A second ranger, 8 miles East of the first ranger, also sights the fire. The bearing from the second ranger to the fire is S 33(degrees). How far is the first ranger from the fire?

67

likes

334 views

Answer to a math question A forest ranger sights a fire to the South. A second ranger, 8 miles East of the first ranger, also sights the fire. The bearing from the second ranger to the fire is S 33(degrees). How far is the first ranger from the fire?

$Expert avatar$

4.7

94 Answers

Let's denote the position of the first ranger as point A, the position of the fire as point F, and the position of the second ranger as point B.

Given:
AB = 8 miles
Angle FBA = 33 degrees

To find the distance between the first ranger (A) and the fire (F), denoted as AF, we can use trigonometry.

We first find the length of side BF using the cosine rule:
cos(33 degrees) = BF / AB
BF = AB * cos(33 degrees)
BF = 8 * cos(33 degrees)

Next, we can use the sine rule to find the distance AF:
sin(33 degrees) = AF / BF
AF = BF * sin(33 degrees)

Calculating the values:
BF = 8 * cos(33 degrees)
BF ≈ 8 * 0.8387
BF ≈ 6.71 miles

AF = BF * sin(33 degrees)
AF ≈ 6.71 * 0.5446
AF ≈ 3.65 miles

Therefore, the first ranger is approximately 3.65 miles away from the fire.

\boxed{AF \approx 3.65 \text{ miles}}

Frequently asked questions (FAQs)

What is the sum of the first 20 natural numbers?

+

What is the formula to find the sum of interior angles in a polygon?

+

Math question: What is the value of log(base 3) 9?

+

New questions in Mathematics

Let 𝑢 = 𝑓(𝑥, 𝑦) = (𝑒^𝑥)𝑠𝑒𝑛(3𝑦). Check if 9((𝜕^2) u / 𝜕(𝑥^2)) +((𝜕^2) 𝑢 / 𝜕(𝑦^2)) = 0

what is 9% of 307

In a random sample of 600 families in the Metropolitan Region that have cable television service, it is found that 460 are subscribed to the Soccer Channel (CDF). How large a sample is required to be if we want to be 95% confident that the estimate of “p” is within 0.03?

6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.

Exercise 1 An ejidal association wishes to determine the distribution for the three different crops that it can plant for the next season on its available 900 hectares. Information on the total available and how many resources are required for each hectare of cultivation is shown in the following tables: Total available resource Water 15,000 m3 Fertilizer 5,000 kg Labor 125 day laborers Requirements per cultivated hectare Corn Soybeans Wheat Water 15 25 20 Fertilizer 5 8 7 Labor** 1/8 1/5 1/4 *The data in fraction means that with one day laborer it will be possible to care for 8, 5 and 4 hectares respectively. * Sales of crops 1 and 3, according to information from the Department of Agriculture, are guaranteed and exceed the capacity of the cooperative. However, soybeans must be limited to a maximum of 150 hectares. On the other hand, the profits for each hectare of crop obtained are estimated at: $7,500 for corn, $8,500 for soybeans and $8,000 for wheat. The objectives are to determine: • How many hectares of each crop must be allocated so that the profit is maximum. R= • The estimated profits for the ejidal cooperative in the next growing season. R=

4+168×10³×d1+36×10³×d2=-12 -10+36×10³×d1+72×10³×d2=0

Two minus log 3X equals log (X over 12)

A teacher has 25 red and yellow counters altogether. She has 4 times as many red counters than yellow counters. How many yellow counters does the teacher have?

Solve equations by equalization method X-8=-2y 2x+y=7

Show work on 4108 divided by 4

2.380× (1+0.05) / 0.95−0.05

viii. An ac circuit with a 80 μF capacitor in series with a coil of resistance 16Ω and inductance 160mH is connected to a 100V, 100 Hz supply is shown below. Calculate 7. the inductive reactance 8. the capacitive reactance 9. the circuit impedance and V-I phase angle θ 10. the circuit current I 11. the phasor voltages VR, VL, VC and VS 12. the resonance circuit frequency Also construct a fully labeled and appropriately ‘scaled’ voltage phasor diagram.

Which statement best describes the key changes in perspectives on inclusion? An inclusive program must consider the unique experiences of every child and family as well as the child's strengths and needs. There is a shift in thinking about individual programs as "inclusive programs" to thinking about inclusion as something that reflects the cultural influence of the family. There is a greater emphasis on barriers to full participation and the acknowledgement that all children are unique and must be fully and meaningfully engaged in a program. In an inclusive program all participants are accepted by their peers and other members of the community.

Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)

If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13

The mean of 4 numbers is 5 and the mean of 3 different numbers is 12. What is the mean of the 7 numbers together? Produce an algebraic solution. Guess and check is acceptable.

A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?

12[4 + (8 + 7) + 5]