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From a balloon 777ft high, the angle of depression to the ranger headquarters is 78.4 degrees. How far is the headquarters from a point on the ground directly below the balloon. (Round to an appropriate number of significant digits)

Sagot :

The give situation can be illustrated as follow:

As you can notice, the vertical distance between the balloon and the ground, the distance between the balloon and the headquartes and distance between vertical line and headquarter form a right triangle.

In order to determine the distance from the headquarter to a point on the ground just below the ballon, use the tanx:

[tex]tanx=\frac{opposite}{adjacent}[/tex]

Here, opposite is the required distance and adjacent is 777ft. x is a complementary angle to 78.4, then, you have:

x + 78.4 = 90

x = 90 - 78.4

x = 11.6

Solve for oppopsite in the equation for tanx, replace the values of the other parameters and simplify:

[tex]\begin{gathered} opposite=adjacent*tanx \\ opposite=(777ft)tan11.6 \\ opposite\approx159.5ft \end{gathered}[/tex]

Hence, the distance from the headquarter to a point on the grpund directly below the balloon is approximately 159.5ft

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