MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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
Clarabelle
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)
Math question: Find the derivative of f(x) = 3x^4 - 2x^2 + 5x - 1 using basic rules of derivatives.
+
What is the limit of (2x + 3) as x approaches 1?
+
What is the probability of drawing a spade or a heart from a standard deck of cards?
+
New questions in Mathematics
Students Ana Beatriz and Paula decided to register on a website with exercises to study for upcoming simulations, but to register on this website, they need to choose a password consisting of five characters, three numbers and two letters (capital letters). or lowercase). Letters and numbers can be in any position. They know that the alphabet is made up of twenty-six letters and that an uppercase letter differs from a lowercase letter in a password. What is the total number of possible passwords for registering on this site?
How much volume of water in MegaLiters (ML) is required to irrigate 30 Hectare crop area with depth of 20mm?
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
3x+2/2x-1 + 3+x/2x-1 - 3x-2/2x-1
The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?
A National Solidarity Bond offers A 5 year bond offering a gross return of 15% Calculate the AER for this investment. (Give your answer to two decimal places, no need for the percent or € sign in your answer)
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
The thermal representation f(x) = 20 times 0.8 to the power of x is known from an exponential function f. Specify the intersection point with the y-axis
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
. What will be the osmotic pressure of a solution that was prepared at 91°F by dissolving 534 grams of aluminum hydroxide in enough water to generate 2.784 ml of solution.
(a) List the set of possible rational zeros of the polynomial function F(x) = 2x3 - 11x2 + 13x - 4. (b) Find all rational zeros of F(x). Only do part B
A company made 150,000 in the first year 145,000 in the second 140,000 in the third year successively during the first decade of this company's existence it made a total of
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.
36 cars of the same model that were sold in a dealership, and the number of days that each one remained in the dealership yard before being sold is determined. The sample average is 9.75 days, with a sample standard deviation of 2, 39 days. Construct a 95% confidence interval for the population mean number of days that a car remains on the dealership's forecourt
-5x=115
You buy a $475,000 house and put 15% down. If you take a 20 year amortization and the rate is 2.34%, what would the monthly payment be?
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
Salut👋🏻 Appuie sur "Créer une nouvelle tâche" pour envoyer ton problème de mathématiques. Un de nos experts commencera à travailler dessus immédiatement !

You might be interested in