Trigonometry Laws of Sines and Cosines 5

Question 1

Heron's formula uses all three sides of a triangle. What is the semi-perimeter s of a triangle with sides 5, 12, and 13?

Accepted Answer

s = 15

Answer

s = 30

Answer

s = 10

Answer

s = 20

Question 2

In triangle ABC, the Law of Cosines gives cos A = −0.5. What is angle A?

Accepted Answer

120°

Answer

60°

Answer

90°

Answer

150°

Question 3

Triangle MNO has M = 25°, N = 110°, and n = 30. What is the length of side m?

Accepted Answer

m = 30·sin 25° / sin 110°

Answer

m = 30·sin 110° / sin 25°

Answer

m = sin 25° / (30·sin 110°)

Answer

m = 30·sin 45° / sin 110°

Question 4

Which statement about the Law of Cosines is TRUE when angle C = 90°?

Accepted Answer

It reduces to the Pythagorean theorem: c² = a² + b²

Answer

It gives c² = a² + b² + 2ab

Answer

It cannot be applied to right triangles

Answer

It gives c² = a² − b²

Question 5

An engineer measures a triangular land parcel: two sides are 80 m and 60 m, and the angle between them is 90°. What is the length of the third side?

Accepted Answer

100 m

Answer

140 m

Answer

70 m

Answer

√(6400 − 3600) = √2800 m

Question 6

Given triangle ABC with a = 13, b = 7, c = 11, which angle is smallest?

Accepted Answer

Angle B (opposite b = 7)

Answer

Angle A (opposite a = 13)

Answer

Angle C (opposite c = 11)

Answer

All angles are equal

Question 7

A triangular sail has sides of 15 ft, 20 ft, and 10 ft. Using the Law of Cosines, what is the cosine of the angle opposite the 20 ft side?

Accepted Answer

(225 + 100 − 400) / 300

Answer

(225 + 400 − 100) / 600

Answer

(100 + 400 − 225) / 400

Answer

(225 + 100 − 400) / 600