Question

Use the drawing tool(s) to form the correct answer on the provided grid.

Lisa and Penny are guests at a beachside hotel. Lisa is laying on a towel at the beach which is 50 feet from the base of the hotel. When she looks up at an angle of 54.5 degrees, she can see her sister Penny waving to her from the hotel window.

Draw a scale representation of the triangle that models the situation and can be solved to find the straight-line distance between Penny and Lisa. Round calculations to the nearest foot. Each unit on the grid represents five feet.

Answer 1

86 ft

Explanation:

You want the straight line distance from a location 50 ft from a hotel to a window that has an angle of elevation of 54.5°.

Cosine

The cosine relation between sides and angles in a right triangle is ...

Cos = Adjacent/Hypotenuse

The 50 ft distance is adjacent to the angle, and we want to find the hypotenuse. Using this equation, we can solve for the length we want:

Hypotenuse = Adjacent/Cos

Application

Using the numbers in the problem statement, we find the straight-line distance to be ...

LW = LH/cos(54.5°) = (50 ft)/0.580703 ≈ 86 ft

The distance between Penny and Lisa is about 86 feet.

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Additional comment

We don't know what drawing tools you have available. The attached diagram was drawn by locating the window at 50tan(54.5°) up from the base of the hotel. The tool provided the length of LW as 86.1.

We could have use a rotation tool to create the angle of 54.5°, or a line graphing tool to draw the line through (50, 0) with slope tan(-54.5°). Then an intersection tool could have located the window at the point of intersection of that line and the y-axis.

The calculation we did above is about the easiest for determining the distance mathematically (not having the tool measure it).

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