What is the slope of the line
1 answer:
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Answer:
Step-by-step explanation:
In this problem, one is given a circle with two secants (that is a line that intersects a circle at two points). One is given certain measurements, the problem asks one to find the unknown measurements.
The product of the lengths theorem gives a ratio between the lengths in the secants. Call the part of the secant that is inside the circle (inside), and the part of the secant between the exterior of the circle and the point of intersection of the secants (outside). The sum of (inside) and (outside) make up the entire secant, call this measurement (total). Remember, there are two secants, () and (
) in this situation. With these naming in mind, one can state the product of the length ratio as the following:
Alternatively, one can state it like the following ratio:
Apply this ratio to the given problem, substitute the lengths of the sides of the secants in and solve for the unknown.
Cross products, multiply the numerator and denominators of opposite sides of the fraction together,
Simplify,
Inverse operations,
Substitute this value into the equation given for the measure of (EF),
Given:
A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.
The distance between plan and mountain is 10 km.
A short time later, the bearing to the mountain becomes 45°.
Here NM is the distance between the plane from the mountain when the second bearing is taken.
We need to find the measure of NM.
The sum of the supplementary angles is 180 degrees.
We know that the sum of all three angles of the triangle is 180 degrees.
Consider the sine law.
Take the equation to find the measure of NM.
Hence the measure of NM is 8.1 km.
The plane is 8.1 km far from the mountain when the second bearing is taken.
