In a square grid, the position of △ABC is shown. Find tanB.
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Step-by-Step Solution
Step 1: Identify Coordinates of Vertices
First, we need to determine the coordinates of the vertices of the triangle from the given square grid. Let's assume the bottom-left corner of the grid is the origin (0,0). Counting the grid units, we find the coordinates of A, B, and C.
Step 2: Draw an Altitude from A to BC
To find tanB, we need to form a right-angled triangle. We can draw an altitude from vertex A perpendicular to the base BC. Let's call the point where the altitude meets BC as D. Since BC lies on the x-axis and A is at (3,4), the point D will be (3,0).
Step 3: Calculate Lengths of Sides in △ ADB
Now we have a right-angled triangle △ADB. We can calculate the lengths of its sides. The length of AD is the difference in the y-coordinates of A and D, which is 4−0=4. The length of BD is the difference in the x-coordinates of B and D, which is 5−3=2.
Step 4: Calculate tan B
In the right-angled triangle △ADB, the side opposite to angle B is AD, and the side adjacent to angle B is BD. The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Substituting the calculated lengths, we get tanB=24=2.