Applications of Sine and Cosine in Problem Solving

What trigonometric law is used to calculate the length of a leaning object when given one side and two angles?

• Law of Sine

• Law of Cosine

• Tangent Law

• Pythagorean Theorem

If the angle of incline from the base is 7 degrees and the angle from the measurement point to the top is 68 degrees, what is the third angle in the triangle?

• 83 degrees

• 105 degrees

• 95 degrees

• 29 degrees

In the second example, what is the angle of elevation when stepping back 100 feet?

• 138 degrees

• 42 degrees

• 8 degrees

• 34 degrees

What is the correct calculation method to find the height of an inaccessible object using two angles of elevation?

• Tangent Law

• Law of Cosine

• Law of Sine

• Pythagorean Theorem

What is the supplementary angle to 42 degrees in the second example?

• 90 degrees

• 142 degrees

• 48 degrees

• 138 degrees

In the third example, what is the included angle between the two traveled paths?

• 25 degrees

• 180 degrees

• 90 degrees

• 115 degrees

What law is used to calculate the direct distance back to the starting point in the third example?

• Law of Sine

• Law of Cosine

• Pythagorean Theorem

• Tangent Law

What is the bearing to return to the starting point from the final position in the third example?

• South 25 degrees West

• North 25 degrees East

• North 67.5 degrees West

• South 67.5 degrees East

How is the angle for the bearing calculated in the third example?

• Sum of two alternate interior angles

• Difference between two supplementary angles

• Difference between two alternate interior angles

• Sum of two supplementary angles

What is the final calculated distance from the starting point in the third example?

• 40.25 miles

• 47 miles

• 30 miles

• 17 miles