Q: Which formula is used to find the area of a triangle when two sides and the included angle are known (SAS)?

$$Area = \\frac{1}{2} ab \\sin C$$

Q: Which of the following is the correct formula for the area of a triangle when the height is known?

$$Area = \\frac{1}{2} \\times base \\times height$$

Q: Why is the formula $$Area = \\frac{1}{2} ab \\sin C$$ valid for any triangle, not just right triangles?

Because $$\\sin C$$ gives the ratio of the height to side $$b$$

Question 1

Given a triangle with sides $$a = 8$$, $$b = 12$$, and included angle $$C = 60^\degree$$, what is the area of the triangle?

Accepted Answer

$$41.6$$

Question 2

Which formula is used to find the area of a triangle when two sides and the included angle are known (SAS)?

Accepted Answer

$$Area = \frac{1}{2} ab \sin C$$

Question 3

A surveyor needs to find the area of a triangular plot with sides $$a = 15 m$$, $$b = 20 m$$, and included angle $$C = 45^\degree. $$What is the area?

Accepted Answer

$$106.1$$

Question 4

If you know two angles and the included side (ASA) of a triangle, which law do you use to find the missing sides before calculating the area?

Accepted Answer

Law of Sines

Question 5

Given triangle $$ABC$$ with $$A = 40^\degree$$, $$C = 60^\degree$$, and $$b = 6$$, what is the first step to find the area?

Accepted Answer

Find the missing side using Law of Sines

Question 6

A triangle has sides $$a = 10$$, $$b = 7$$, and included angle $$C = 120^\degree. $$What is the area?

Accepted Answer

$$60.6$$

Question 7

Which of the following is the correct formula for the area of a triangle when the height is known?

Accepted Answer

$$Area = \frac{1}{2} \times base \times height$$

Question 8

A triangle has $$A = 30^\degree$$, $$b = 10$$, $$B = 80^\degree. $$What is the area of the triangle?

Accepted Answer

$$29.2$$

Question 9

Why is the formula $$Area = \frac{1}{2} ab \sin C$$ valid for any triangle, not just right triangles?

Accepted Answer

Because $$\sin C$$ gives the ratio of the height to side $$b$$

Question 10

A triangle has sides $$a = 9$$, $$b = 12$$, and included angle $$C = 75^\degree. $$What is the area?

Accepted Answer

$$52.1$$

Question 11

If you are given $$A = 50^\degree$$, $$B = 60^\degree$$, and $$c = 8$$, what is the correct sequence to find the area?

Accepted Answer

Use Law of Sines to find $$a or$$ $$b$$, then use $$Area = \frac{1}{2} ab \sin C$$

Question 12

A triangle has sides $$a = 5$$, $$b = 7$$, and included angle $$C = 90^\degree. $$What is the area?

Accepted Answer

$$17.5$$

Question 13

Which of the following is NOT a valid method for finding the area of a triangle given two angles and the included side?

Accepted Answer

Using Heron's formula directly

Question 14

A triangle has $$A = 45^\degree$$, $$B = 55^\degree$$, and $$c = 10. $$What is the area?

Accepted Answer

$$28.7$$

Question 15

In a triangle, if $$a = 6$$, $$b = 8$$, and $$C = 30^\degree$$, what is the area?

Accepted Answer

$$24.0$$

Area of SAS & ASA Triangles: Trigonometric Applications

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