A superhero is running toward a skyscraper to stop a villain from getting away. As he is moving, he looks up at the top of the building and his line of sight makes a 33.0° angle with the ground. After having moved 300 m, he looks at the top of the building again, and notices that his line of sight makes a 52.0° angle with the horizontal. How tall is the skyscraper?

Question

A superhero is running toward a skyscraper to stop a villain from getting away. As he is moving, he looks up at the top of the building and his line of sight makes a 33.0° angle with the ground. After having moved 300 m, he looks at the top of the building again, and notices that his line of sight makes a 52.0° angle with the horizontal. How tall is the skyscraper?

Answer 1

draw picture

get angles in first triangle
180 - 52 = 128

180 -128 - 33 = 19 which is angle opposite the 300

then law of sines
sin 19/300 = sin 33/second slope up
so
second slope = 300 (sin 33 / sin 19)
= 502 meters

then right triangle
sin 52 = h/502
h = 395 meters
four football fields high !!!

Answer 2

To determine the height of the skyscraper, we can use the concept of trigonometry and set up a right triangle.

Let's consider the initial position of the superhero as point A, the final position as point B, and the top of the skyscraper as point C. The distance between the initial and final position, 300 m, is the base of the triangle (AB). The height of the skyscraper, which we want to find, is the vertical side of the triangle (BC).

We can start by finding the angle A. In the initial position, the superhero's line of sight makes a 33.0° angle with the ground. Since the line of sight is vertical in respect to the ground, angle A is the complement of angle A', which is 90° - 33.0° = 57.0°.

Next, let's find angle B. In the final position, the superhero's line of sight makes a 52.0° angle with the horizontal. Since angle B is the complement of angle B', we have 90° - 52.0° = 38.0°.

Now, we have angle A, angle B, and the length of side AB (base of the triangle). To find the height of the building (BC), we can use the tangent function.

The tangent of angle A is equal to the opposite side (BC) divided by the adjacent side (AB). So, we have the equation:

tan(A) = BC / AB

Substituting the values we know:

tan(57.0°) = BC / 300m

We can rearrange the equation to solve for BC:

BC = tan(57.0°) * 300m

Using a scientific calculator or trigonometric table, we find:

BC ≈ 404.57 m

Therefore, the height of the skyscraper is approximately 404.57 meters.