Question

Lisa is 800 meters from the base of a mountain. From where she stands, she measures the angle of elevation to the peak of the mountain to be 38 degree. She then walks to the base of the mountain and measures the new angle of elevation, this time getting 49 degree.

How far is Lisa from the peak of the mountain when she is standing at its base?
Do not round during your calculations. Round your final answer to the nearest meter.

Answer 1

To find the distance from Lisa to the peak of the mountain when she is standing at its base, we can use trigonometry to solve for x using the concept of angles of elevation.

Step-by-step explanation:

To find the distance from Lisa to the peak of the mountain when she is standing at its base, we can use the concept of trigonometry. Let's assume the distance from Lisa to the peak of the mountain when she is standing at its base is x meters.

Using the first angle of elevation, we can set up the trigonometric equation: tan(38°) = 800 / x. Solving for x, we have: x = 800 / tan(38°).

Next, using the second angle of elevation, we can set up another trigonometric equation: tan(49°) = 800 / (x + 800). Solving for x, we have: x = 800 / tan(49°) - 800.

Now, we can calculate the distance x by substituting the values into the equations and rounding the final answer to the nearest meter.

Answer 2

Lisa is 2581 \,\text{m}2581m2581, start text, m, end text from the peak of the mountain when she is standing at its base.

Step-by-step explanation: 2581