What is the distance from point D to point C?
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
<u>Application of Right Triangles </u>
The right triangles have an internal angle of 90°, we can take advantage of it because the fundamental trigonometric functions can be expressed to relate angles and lengths in a right triangle.
Please refer to the image below to understand the upcoming relations and variables. The lower triangle has an angle \theta and h_h and D are the opposite and adjacent legs respectively, then:
Where h_h is the height of the tower. We can solve:
For the big triangle:
Where is 8° and
is the height of the hill. Knowing that:
We replace it into the above equation
We have an equation in , but we need to expand the tangent of a sum of angles:
Rearranging
Multiplying
Simplifying, we have a second-degree equation for tan\theta
Using the known values D=110, ht=30,
Solving the equation, we get two answers:
This solution is not feasible, since the angle cannot exceed 90° or go below 0°, thus the other answer
is the correct option. Computing the angle of inclination of the hill:
