Question

Someone must have beaten me here. Devora thinks, dismayed by the empty treasure chest. Then, just as she's about to close the lid, she notices a map (shown below). "Curse these trig-loving pirates!" Devora mutters as she looks at the map. Then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 484848 meters along the way. After performing a calculation, Devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 898989 meters to the treasure. Supposing that the angle at the Cave entrance is acute and that Devora's calculations were correct, how many degrees did she turn? Do not round during your calculations. Round your final answer to the nearest degree.

Answer 1

Explanation:

Answer 2

Based on the assumption that the angle of the triangle at the cave entrance is a right angle, the angle Devora turned before walking to the treasure chest is approximately 57 degrees.

Explanation:

A sketch of the triangle formed is attached where E is the entrance of the cave, C is the treasure chest and T is the treasure itself.

Using the cosine trigonometric ratio, we have that

`\cos \theta = (484848)/(898989) = 0.5393`

Finding the arccosine of 0.5393 gives
`57.36^0`