A surveyor is trying to measure the distance BC across a river. From point B, directly across from point C, he walks along the bank to point A from which he sites C at an angle of 45o. If the distance AB is 120 yards, how far is it across the river?
Question
A surveyor is trying to measure the distance BC across a river. From point B, directly across from point C, he walks along the bank to point A from which he sites C at an angle of 45o. If the distance AB is 120 yards, how far is it across the river?
Solution
This problem can be solved using trigonometry. Here are the steps:
-
Identify the triangle: In this case, we have a right triangle ABC with a 45-degree angle at point A.
-
Use the properties of a 45-degree triangle: In a 45-degree triangle, the lengths of the two legs are equal. This is because in a 45-45-90 triangle, the sides are in the ratio 1:1:√2.
-
Apply this to the problem: Since the distance AB is 120 yards, and angle A is 45 degrees, the distance BC (across the river) is also 120 yards.
So, the distance across the river is 120 yards.
Similar Questions
A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35°35° . How wide is the river?
Greg and Lucy are standing on a riverbank, at points A and B respectively. (See the figure below.) Lucy is 230 meters from a house located across the river at point C. Suppose that angle A (angle BAC) is 47°, and angle B (angle ABC) is 75°. How far are Greg and Lucy standing from one another? Round your answer to the nearest tenth of a meter.47°75°ABC230mmeters CheckSave For LaterSubmit Assignment
A surveyor needs to find the length from point A to point C across a lake as shown in the figure below. The measurements of which of the following angles and side lengths are sufficient for the surveyor to determine the length of 𝐴𝐶‾AC using only the law of sines?
Hong wants to measure the width of a river. He marks off two right triangles, as shown in the figure. The base of the larger triangle has a length of 63m, and the base of the smaller triangle has a length of 35m. The height of the smaller triangle is 20.2m. How wide is the river? Round your answer to the nearest meter.
Amita is standing at point A facing north directions then she turns at angle 90 at her right and once again travels the same distance.She reaches point B.Now she takes a run 90 at her left and walks for 3 kilometers and reaches at point C.What is the direction of B and C with respect to point A
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.