A black bordering Sapphire St. is a right triangle. You start walking around the block, taking 125 paces on sapphire st. and 102 paces on Diamond st.
a.) At what angle do Diamond and Sapphire Street Intersect ?
To find the angle at which Diamond Street and Sapphire Street intersect, we can use the concept of trigonometry. The angle of intersection between two streets can be determined by finding the inverse tangent of the ratio of the lengths of the two sides of the triangle.
Given that Sapphire Street is the side opposite the angle we want to find and Diamond Street is the adjacent side, we can use the tangent function to find the angle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the length of Sapphire Street (125 paces) and the adjacent side is the length of Diamond Street (102 paces). Therefore, the tangent of the angle at which Diamond and Sapphire Street intersect can be calculated as:
tan(angle) = opposite/adjacent
tan(angle) = 125/102
To find the angle, we can take the inverse tangent (also known as the arctangent) of both sides:
angle = arctan(tan(angle))
angle = arctan(125/102)
To find the value of this angle, you can use a scientific calculator or an online calculator that offers trigonometric functions. Simply input the ratio of 125/102 and calculate the arctangent.
Keep in mind that the angle obtained will be in radians. If you wish to convert it to degrees, you can multiply it by (180/π) to get the angle in degrees.