Question

A 20-foot tall flagpole is leaning towards a house. If the flagpole makes an 85 degree angle with the ground and the angle of elevation from the base of the house to the top of the pole is 55 degrees, find the distance from the base of the flagpole to the house

Answer 1

Answer:

Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.

Step-by-step explanation:

We are given the following in the question:

Height of pole = 20 foot

Angle between pole and ground = 85 degrees

Angle of elevation from the base of the house to the top of the pole = 55 degrees

Then, the third angle of the triangle can be found as:

Angle sum property of triangle: The sum of the three angles of a triangle is 180 degrees.

$x + 85 + 55 = 180\\x = 180 - 140\\x = 40^\circ$

Thus, by the sin rule, we can write:

$\dfrac{\text{Distance from the base of the flagpole to the house}}{\sin 55} = \dfrac{20}{\sin 40}\\\\\Rightarrow \text{Distance from the base of the flagpole to the house} = 20\times \dfrac{\sin 55}{\sin 40}\\\\=20\times \dfrac{0.82}{0.64} = 25.625$

Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.