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Two boats start their journey from the same point A and travel along directions AC and AD, as shown

What is the distance, CD, between the boats?

0 213.2 ft
O 115.5 ft
0 230.9 ft
0 346.4 ft​


Two Boats Start Their Journey From The Same Point A And Travel Along Directions AC And AD As Shown What Is The Distance CD Between The Boats 0 2132 Ft O 1155 Ft class=

Sagot :

Answer:

[tex]346.4\text{ ft}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the side lengths are in a ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle.

In [tex]\triangle ABD[/tex], the side marked as 300 ft, AB, is the side opposite to the 30 degree angle. Therefore, BD must equal [tex]300\sqrt{3}\text{ ft}[/tex].

To find CD, we can subtract BC from BD. Notice that [tex]\triangle ABC[/tex] is also a 30-60-90 triangle. Therefore, since BC is the side opposite to the 30 degree angle, BC must equal [tex]\frac{300}{\sqrt{3}}=\frac{300\sqrt{3}}{3}}\text{ ft}[/tex]

Thus, the length of CD is equal to:

[tex]CD=BD-BC,\\CD=300\sqrt{3}-\frac{300\sqrt{3}}{3}=346.410161514\approx \boxed{346.4\text{ ft}}[/tex]

Answer:

346.4 ft

Step-by-step explanation: