Diana works in a building that is 130 feet tall. she is outside, looking up at the building at an angle of 37° from her feet to the top of the building.
if diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? round the answer to the nearest tenth of a foot.
10.3 ft
17.6 ft
30.2 ft
97.2 ft

Step-by-step explanation:

Givens

If we draw the situation, it would be like the one presented in the image attached.

To find the answer, we need to find the distance when the angle is 37° and the distance when the angle is 40°, to do so, we have to use the trigonometric reasons.

In this case, we have the angle and its opposite leg. In order to find the horizontal distance, we need to use the tangent

Then, the angle changes to 40°, but the height of the building remains the same obsviously

Now, we need to find the difference,

Therefore, the right answer is 17.6ft, the second choice.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction