Question

Alex is standing 60 feet from the base of a flagpole. He measures the angle of elevation to the top of the pole as 35º. Vera is 36 feet closer to the base of the flagpole on a straight level path. Find the angle of elevation from the point Vera is standing to the top of the flagpole to the nearest tenth of a degree.

Is it 49.4 degrees?

Answer 1

To find the angle of elevation from the point Vera is standing to the top of the flagpole, we can use trigonometry. Assuming the distance between Vera and the base of the flagpole is x feet, we can calculate the angle with the tangent function.

Step-by-step explanation:

To find the angle of elevation from the point Vera is standing to the top of the flagpole, we can use trigonometry. Let's assume that the distance between Vera and the base of the flagpole is x feet. We can create a right triangle with the height of the flagpole, the distance between Alex and the base of the flagpole, and the distance between Vera and the base of the flagpole.

Using the tangent function, we can set up the equation: tan(angle) = height / distance.

Substituting the values, we have: tan(angle) = height / (60 + x). Rearranging the equation, we can solve for x: tan(angle) * (60 + x) = height.

Plugging in the values, we have: tan(35) * (60 + x) = height. Solving for x, we find that x is approximately 23.3 feet. Now, we can find the angle of elevation from Vera's point by using the same equation with the new values: tan(angle) = height / (36 + x). Plugging in the values, we find that the angle of elevation is approximately 49.4 degrees.

Answer 2

49.4 degrees

Step-by-step explanation:

In Triangle AXY,

`Tan 35^0=(|XY|)/(60) \\|XY|=60*Tan 35^0=42.01\:feet\\$Therefore, Height of the pole=42.01 \:feet`

We want to determine the angle of elevation from the point Vera is standing to the top of the flagpole, which is the angle at V in the diagram.

In Triangle XVY

|VY|=36 feet

`Tan \theta=(|XY|)/(|VY|) \\Tan \theta=(42.01)/(36)\\ \theta=arctan((42.01)/(36))\\ \theta=49.4^0`

Therefore, the angle of elevation from the point Vera is standing to the top of the flagpole is 49.4 degree to the nearest tenth of a degree.