Question

To indirectly measure the distance across a lake, Isaac makes use of a couple landmarks at points C and D. He measures BC, DE, and EF as marked. Find the distance across the lake CD, rounding your answer to the nearest hundredth of a meter.

Answer 1

The distance across a river can be calculated using trigonometry by measuring an angle and the length of a baseline walked along the riverbank. The tangent function is used to find the width of the river based on these measurements.

Step-by-step explanation:

To find the distance across the lake or to measure the width of a river, surveyors use trigonometry. In the scenario provided, starting from a point directly across from a tree, the surveyor walks 100 m along the river and then measures an angle of 35° to the tree. Assuming this forms a right-angled triangle, the distance across the river (opposite side of the angle) can be calculated using the tangent function:

tan(θ) = opposite/adjacent

So,

tan(35°) = distance/100 m

distance = 100 m × tan(35°)

Using a calculator to find tan(35°) and multiplying by 100 gives us the distance across the river. This method relies on the concept of parallax, which is the apparent change in position of an object when viewed from different locations. It's important to use a calculator that is set to degree mode for this calculation.