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Pachacha [2.7K]
3 years ago
10

Does anyone know the answer?

Mathematics
1 answer:
Mashcka [7]3 years ago
4 0

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.

tan \theta = \frac{oppositeside}{adjacent side}.

Step 2:

The length of the opposite side = 42 meters.

The length of the adjacent side = (24 + x) meters.

tan \theta = \frac{oppositeside}{adjacent side}, tan 48 = \frac{42}{24+x}, tan 48 = 1.1106.

1.1106 (24+x) = 42, 26.6544 + 1.1106x = 42.

1.1106x = 42 - 26.6544 = 15.3456, x = \frac{15.3456}{1.1106} = 13.8173.

So the distance between C and D is 13.8173 meters.

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