Q:

John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground opposite a big tree. The steps John would use to find the measure he wants are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.The steps John would use to measure the width of the stream are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.1. Step 1 5John measures the distance between the two stakes. 2. Step 2 2John uses a compass to walk away from the stake at a right angle. 3. Step 3 4John multiplies the distance between the two stakes by 1.7 to find the distance. 4. Step 4 3John drives a second stake in the ground. 5. Step 5 1On the path John walks until he finds a line of sight to the tree that equals 60 degrees. 6. Step 6 6John drives a stake opposite the tree to establish a line between two points.

Accepted Solution

A:
John's method to determine the width of the stream uses the knowledge that the tangent of 60Β° is approximately 1.7.The proper sequence John would use to find the width of the stream are;Step 1; John drives a stake opposite the tree to establish a line between two pointsStep 2; John uses a compass to walk away from the stakes at a right angleStep 3; On the path John walks until he finds a line of sight to the tree that equals 60 degrees Step 4; John drives a second stake in the groundStep 5; John measures the the distance between the two stakesStep 6; John multiplies the distance between the two stakes by 1.7 to find the distance.Reasons:The steps that can be used to measure the width of the stream are;Step 1: Drive a stake opposite the tree on the other side of the stream.Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60Β°.Step 4; At the point where the line of sight to the tree is 60Β°, a second stake is driven in the ground. Step 5; Measure the distance between the stakes that are placed in the ground.Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60Β°) β‰ˆ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.[tex]\displaystyle tan(60^{\circ}) = \mathbf{\frac{Width \ of \ stream}{Distance \ between \ stakes}}[/tex]The possible question options are;John measures the the distance between the two stakesJohn uses a compass to walk away from the stakes at a right angleJohn multiplies the distance between the two stakes by 1.7 to find the distanceJohn drives a second stake in the groundOn the path John walks until he finds a line of sight to the tree that equals 60 degrees John drives a stake opposite the tree to establish a line between two points.Learn more about trigonometric ratios here: