trigonometry math

Question

Tim looks straight north and sees the top of a building 40 m distant at an angle of elevation of 20°. He looks straight west from the same position and sees the top of a building 80 m distant at an angle of elevation of 14 °. Sketch the situation.

Which building is taller, and by how much?

What is the straight-line distance between the top points of the buildings that Tim used to measure?

What is the angle of elevation from the top of the lower building to the top of the higher building?

Answer 1

For determining how much taller each building is than the one Tim is standing on, we will use the tangent function. tan A = opposite / adjacent = a / b

North building.. A = 20 degrees. Tan A = 0.36397023 = a / 40.. a = 40m * 0.36397023 = 14.558m

West building.. A = 14 degrees. Tan A = 0.249328 = a / 80.. a = 80m * 0.249328 = 19.946m

The West building is 5.38m taller.

For determining the distance between the two buildings that Tim is looking at, we will use the pythagorean theorem. a² + b² = c²

Where a = 40m, and b = 80m

1600 + 6400 = 8000

The square root of 8000 is 89.442. This is the straight line distance between the two buildings.

For determining the angle of elevation between the two buildings, we will again use the tangent function as well as the arctangent function.

The adjacent side of the triangle is the distance between the two buildings (89.442) and the opposite side is the height difference between them (5.38).

tan A = opposite / adjacent = 5.38 / 89.442 = 0.06015

tan^-1 0.06015 = 3.442°