Trigonometry and Triangle Properties

Mr. Allen presents a challenge problem to find the perimeter of triangle ABC, given certain angles and a side length. The problem is not a right triangle, so he demonstrates how to solve it using right triangle trigonometry by dropping an altitude to create two right triangles. He calculates side lengths using trigonometric functions like cosine and sine, and also shows an alternative method using the Pythagorean theorem. The importance of rounding only once is emphasized to avoid compounding errors. The final perimeter is calculated, and Mr. Allen concludes the lesson.

What are the given angles in triangle ABC?

• 30° and 60°

• 45° and 55°

• 40° and 50°

• 35° and 50°

What is the length of side BC in the problem?

• 16T

• 10T

• 12T

• 14T

Why can't right triangle trigonometry be used initially in this problem?

• Because the sides are not known

• Because the triangle is too large

• Because the angles are too small

• Because the triangle is not a right triangle

What is the purpose of dropping an altitude in the triangle?

• To divide the triangle into three parts

• To measure the angles

• To find the midpoint

• To create two right triangles

Which trigonometric function is used to find the first segment (x) from the 50° angle?

• Sine

• Cosine

• Tangent

• Secant

Why is it important not to round intermediate values during calculations?

• To use fewer digits

• To avoid compounding errors

• To make the calculations easier

• To save time

Which trigonometric function is used to find the second segment (y) from the 50° angle?

• Tangent

• Cosine

• Cotangent

• Sine

What is the alternative method mentioned for finding the second segment (y)?

• Using the Pythagorean theorem

• Using the Law of Cosines

• Using the Law of Sines

• Using the Law of Tangents

What is the final calculated perimeter of triangle ABC?

• 47.87 feet

• 45.87 feet

• 50.87 feet

• 48.87 feet

What is the key takeaway regarding rounding in trigonometric calculations?

• Round to the nearest whole number

• Do not round at all

• Round only once at the end

• Round after each step