The points C and D are 13.8173 meters apart.
Step-by-step explanation:
Step 1:
Assume the distance between points C and D is x. So the distance from B to D is (x + 24) m.
In the triangle, the given angle is 48°, the opposite side, AB's length is 42 meters. The adjacent side's length is (24 + x) meters. To determine the x's length, we determine the tan of the angle. To calculate the tan of an angle, we divide the opposite side's length by the adjacent side's length.
[tex]tan \theta = \frac{oppositeside}{adjacent side}.[/tex]
Step 2:
The length of the opposite side = 42 meters.
The length of the adjacent side = (24 + x) meters.
[tex]tan \theta = \frac{oppositeside}{adjacent side}, tan 48 = \frac{42}{24+x}, tan 48 = 1.1106.[/tex]
[tex]1.1106 (24+x) = 42, 26.6544 + 1.1106x = 42.[/tex]
[tex]1.1106x = 42 - 26.6544 = 15.3456, x = \frac{15.3456}{1.1106} = 13.8173.[/tex]
So the distance between C and D is 13.8173 meters.
