Question

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.

Answer 1

The tan angle opposite to opposite side and the hypotenuse is the ratio of opposite side to the hypotenuse side.

The distance between the building and Diana after walking is,17.6 ft.

How to calculate the sides of right angle?

The tan angle opposite to opposite side and the hypotenuse is the ratio of opposite side to the hypotenuse side.

Given information-

The height of the building is 130 ft.

Initial angle of the Diana with the building when she looks up, is 37 degrees.

The angle when, Diana walks forward looking to the top of the building changes to 40°.

Suppose Diana was x meter away, from the building when the angle was 37 degrees.

The  Diana walks forward and her angle looking to the top of the building changes to 40°.

As tan angle is the ratio of opposite side to the hypotenuse. Therefore

$\begin{aligned}\tan (37^o)&=\dfrac{130}{x}\\x&=172.5\\\end$

Now suppose the distance covered by Diana after walking is y ft. Thus again by the right angle property,

$y=\dfrac{130}{\tan40}\\y=154.9$

As the initial distance from building is 172.5 fr and distance covered by Diana is 154.9 ft. Thus the distance between the building and Diana after walking is,

$d=172.5-154.9\\d=17.6\rm ft$

Hence the distance between the building and Diana after walking is,17.6 ft.

Learn more about the trigonometry here;

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