Question

Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230° and boat B has a bearing of 120°. Emma estimates the angles of depression to be about 38° for boat A and 35° for boat B. How far apart are the boats to the nearest meter?

243

likes
1214 views

Answer to a math question Emma is on a 50 m high bridge and sees two boats anchored below. From her position, boat A has a bearing of 230° and boat B has a bearing of 120°. Emma estimates the angles of depression to be about 38° for boat A and 35° for boat B. How far apart are the boats to the nearest meter?

Expert avatar
Jayne
4.4
103 Answers
In this diagram, point A represents Emma's position on the bridge, point B represents boat A, and point C represents boat B. We know that the height of the bridge is 50 meters, and the angles of depression to boats A and B are 38° and 35°, respectively. We also know that the bearings of boats A and B are 230° and 120°, respectively. We can use the tangent function to find the distances from Emma to boats A and B. For boat A, we have: tan(38°) = 50 / d_A Solving for d_A, we get: d_A = 50 / tan(38°) = 64.1 meters Similarly, for boat B, we have: tan(35°) = 50 / d_B Solving for d_B, we get: d_B = 50 / tan(35°) = 71.4 meters Now that we know the distances from Emma to boats A and B, we can use the Law of Cosines to find the distance between the two boats. The Law of Cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C) where c is the distance between the two points, a and b are the distances to the two points from a third point, and C is the angle between the lines connecting the third point to the two other points. In this case, we have: c = d_A + d_B a = 50 meters b = 50 meters C = 110° Substituting these values into the Law of Cosines, we get: (d_A + d_B)^2 = 50^2 + 50^2 - 2 * 50 * 50 * cos(110°) Solving for c, we get: c = sqrt((d_A + d_B)^2 - 50^2 - 50^2 + 2 * 50 * 50 * cos(110°)) Plugging in the values for d_A and d_B, we get: c = sqrt((64.1 + 71.4)^2 - 50^2 - 50^2 + 2 * 50 * 50 * cos(110°)) Evaluating this expression, we get: c = 111.4 meters Therefore, the distance between the two boats is approximately 111 meters to the nearest meter.

Frequently asked questions (FAQs)
Math question: What is the square root of 121?
+
What is the derivative of f(g(x)) with respect to x, where f(u) = sin(u) and g(x) = e^x + x^2?
+
What is the vertex form of a parabola with a vertex at (2, -5) and opens downwards
+
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
How to find the value of x and y which satisfy both equations x-2y=24 and 8x-y=117
A=m/2-t isolate t
10! - 8! =
the value of sin 178°58'
(2x+5)^3+(x-3)(x+3)
Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24
Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
Next%C3%B3n%2C+we+are+given+a+series+of+Tri%C3%A1angles+Right%C3%A1angles+%3Cbr%2F%3Ey+in+each+one+of+them+ are+known+2%28two%29+measurements+of+sides.+%3Cbr%2F%3Elet's+determine+all+trigonom%C3%A9tric+ratios.
When Sara was 15 years old, an uncle left her as inheritanceà a sum of 10,000 euros which he invested in a bank that applies the interest rate of 2,5% annual. Today Sara is 18 years and wants to buy a'car, how much she can ò withdraw from the bank?
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all centers of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
simplify w+[6+(-5)]
In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.