Calculating Distances in Triangles

The video tutorial explains how to calculate the distance across a lake by using the law of sines. It begins by setting up a triangle with known angles and sides, then applies trigonometric principles to find unknown angles and the desired distance. The process involves calculating angles B and C, and finally determining the length of side C, which represents the distance across the lake.

What is the primary goal of the surveyor in the problem?

• To measure the depth of the lake

• To find the distance across the lake

• To calculate the area of the triangle

• To determine the height of point C

Which angle is initially known in the triangle formed by points A, B, and C?

• Angle A

• Angle B

• Angle C

• None of the angles

What mathematical law is used to find the measure of angle B?

• Law of Tangents

• Law of Sines

• Pythagorean Theorem

• Law of Cosines

Which trigonometric function is used to solve for angle B?

• Secant

• Tangent

• Cosine

• Sine

After finding angle B, how is angle C determined?

• By using the Law of Cosines

• By subtracting angles A and B from 180 degrees

• By measuring directly

• By using the Pythagorean Theorem

What is the sum of the interior angles of any triangle?

• 180 degrees

• 360 degrees

• 270 degrees

• 90 degrees

Why is it better to use angle A for the second application of the Law of Sines?

• Because angle A is an approximation

• Because angle A is larger

• Because angle A is an exact measure

• Because angle A is smaller

What is the final step in calculating the distance across the lake?

• Using the Pythagorean Theorem

• Dividing by sine of angle A

• Dividing by sine of angle C

• Using the Law of Cosines

To how many decimal places is the final distance across the lake rounded?

• One decimal place

• Two decimal places

• Three decimal places

• Four decimal places

What is the approximate distance across the lake?

• 97 yards

• 514 yards

• 386 yards

• 682 yards