Matthew parks his car between Karen’s and Patrick’s apartment buildings. The car is 46 m in front of

Question

Matthew parks his car between Karen’s and Patrick’s apartment buildings. The car is 46 m in front of

Karen’s apartment building. The angle of elevation from the car to the top of the building is 40°. Matthew’s
car is 39 m away from Patrick’s apartment building. The angle of elevation from the car to the top of the
building is 50°.
a) Determine the height of each building, to the nearest metre.
b) State which building is taller, and by how much.

Answer 1

a) Let's call the height of Karen's building "h" and the height of Patrick's building "k". We can use trigonometry to solve for each height.

For Karen's building:

tan(40°) = h/46

h = 46 tan(40°) ≈ 41 m

For Patrick's building:

tan(50°) = k/39

k = 39 tan(50°) ≈ 50 m

So Karen's building is approximately 41 m tall and Patrick's building is approximately 50 m tall.

b) Therefore, Patrick's building is taller than Karen's building by approximately 9 meters.

Answer 2

To solve this problem, we can use trigonometry, specifically the tangent function.

Let's first find the height of Karen's apartment building.

Step 1: Use the tangent function to find the height of Karen's building.
tan(40°) = height of Karen's building / 46 m

Rearrange the equation to solve for the height:
height of Karen's building = tan(40°) * 46 m

Calculating this value, we get:
height of Karen's building = (0.8391) * 46 m
height of Karen's building ≈ 38.575 m ≈ 39 m (to the nearest meter)

So, the height of Karen's building is approximately 39 meters.

Step 2: Repeat the same process to find the height of Patrick's building.
tan(50°) = height of Patrick's building / 39 m

Rearrange the equation to solve for the height:
height of Patrick's building = tan(50°) * 39 m

Calculating this value, we get:
height of Patrick's building = (1.1918) * 39 m
height of Patrick's building ≈ 46.493 m ≈ 46 m (to the nearest meter)

So, the height of Patrick's building is approximately 46 meters.

For part a), the height of Karen's building is 39 meters, and the height of Patrick's building is 46 meters.

For part b), Patrick's building is taller by (46 - 39) = 7 meters.