Before the widespread introduction of electronic devices to measure distance, surveyors used a subtense bar to measure a distance z that is not directly measurable. A subtense bar is a bar of known length h with marks or "targets" at either end. The surveyor measures the angle 0 formed by the location of the surveyor's scope and the top and bottom of the bar (this is the angle subtended by the bar). Since the angle and height of the bar are known, right triangle trigonometry can be used to find this horizontal distance. Alternatively, if the distance from the surveyor to the bar is large, then the distance can be approximated by the radiusrof the arc s intercepted by the bar. Surveyor ..... s=h Subtense bar A surveyor uses a subtense bar to find the distance across a river. If the angle of sight between the bottom and top marks on a 2 m bar is 45'28 ", approximate the distance across the river between the surveyor and the bar. Round to the nearest meter.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.