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
104 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)
What is the volume of a rectangular solid with length L, width W, and height H? (
+
What is the value of (2^3 * 2^-2) / (2^4)^-1?
+
What is the value of x in the equation log(base 3) x = 4?
+
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?
The time it takes for a person to travel 300 m is 15 minutes. What is their speed in meters per second?
A car tire can rotate at a frequency of 3000 revolutions per minute. Given that a typical tire radius is 0.5 m, what is the centripetal acceleration of the tire?
(x^2+3x)/(x^2-9)=
-8+3/5
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
solve the following trigo equation for 0°<= x <= 360°. sec x =-2
*Question!!* *Victory saved 3,000 in first bank and 2,000 Naira in union bank PSC with interest rate of X% and Y% per annual respectively his total interest in one year is #640. If she has saved 2,000 naira with first bank and 3,000 naira in union bank for same period she would have made extra 20# as additional interest, then find the value of X and Y
Elliot opened a savings account and deposited $5000.00 as principal. The account earns 4% interest, compounded annually. How much interest will he earn after 5 years? Round your answer to the nearest cent.
B - (-4)=10
Substitute a=2 and b=-3 and c=-4 to evaluate 2ac/(-2b^2-a)
What is 28 marks out of 56 as a percentage
The ninth term of a given geometric progression, with reason q , is 1792, and its fourth term is 56. Thus, calculate the fourth term of another geometric progression, whose ratio is q +1 and whose first term is equal to the first term of the first P.G. described.
The function h(t)=-5t^2+20t+60 models the height in meters of a ball t seconds after it’s thrown . Which describe the intercepts and vertex of this function
Kaya deposits 25,000 into an account that earns 3% interest compounded monthly. How much does Kaya have in the account after 6 years 8 months? Round to the nearest cent. 32,912.50 30,000 29,923.71 30,527.45
A 20,000 kg school bus is moving at 30 km per hour on a straight road. At that moment, it applies the brakes until it comes to a complete stop after 15 seconds. Calculate the acceleration and the force acting on the body.
What is the total amount due and the amount of interest on a 3-year loan of $1,000 at a simple interest rate of 12% per year?
Calculate NPV, IRR and PAYBACK through a cash flow for a period of five years, with discount rate of: a) 10% b) 12% c) 15% initial annual cost $41,400,000
simplify w+[6+(-5)]
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart