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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.

Respuesta :

calculista

Answer:

[tex]543\ m[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ABC

Find the length side BC (the high of the mountain)

[tex]tan(38\°)=\frac{BC}{AC}[/tex]

substitute the values and solve for BC

[tex]BC=(AC)tan(38\°)[/tex]

[tex]BC=(800)tan(38\°)\ m[/tex]

step 2

In the right triangle DBC

Find the length side DC

[tex]tan(49\°)=\frac{BC}{DC}[/tex]

[tex]DC=\frac{BC}{tan(49\°}[/tex]

substitute the value of BC

[tex]DC=\frac{(800)tan(38\°)}{tan(49\°}=543\ m[/tex]

Ver imagen calculista

Answer:

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

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