Area of a Triangle Using Trigonometry

Question 1:What is the formula for the area of a triangle using trigonometry?

(A) (1/2) × a × b × sin(C)
(B) (1/2) × a × b × cos(C)
(C) (1/2) × a × b × tan(C)
(D) (1/2) × a × b × cot(C)

Question 2:If two sides of a triangle are 8 cm and 10 cm, and the included angle is 30°, what is the area?

(A) 40 cm²
(B) 20 cm²
(C) 10 cm²
(D) 16 cm²

Question 3: What is the maximum value of sin(C) in the formula for the area of a triangle?

(A) 0.5
(B) 0.707
(C) 1
(D) 1.5

Question 4:A triangle has sides 7 cm and 9 cm with an included angle of 90°. What is its area?

(A) 21 cm²
(B) 45 cm²
(C) 27 cm²
(D) 31.5 cm²

Question 5:Which trigonometric function is used in the formula for the area of a triangle?

(A) Sine
(B) Cosine
(C) Tangent
(D) Cosecant

Question 6:If the included angle of a triangle is 0°, what is the area of the triangle?

(A) Maximum
(B) Zero
(C) Negative
(D) Undefined

Question 7:If a triangle has an area of 24 cm², sides of 6 cm and 8 cm, what is sin(C)?

(A) 0.5
(B) 0.707
(C) 1
(D) 1.5

Question 8:What is the area of an equilateral triangle with a side length of s using trigonometry?

(A) s²/2
(B) s²/3
(C) s²/6
(D) (s²√3)/4

Question 9:If a triangle has sides 12 cm and 15 cm, and an included angle of 45°, what is the area?

(A) 63.64 cm²
(B) 90 cm²
(C) 45 cm²
(D) 70 cm²

Question 10:The area of a triangle using trigonometry is best used when we know…?

(A) All three sides
(B) Two sides and the included angle
(C) One side and two angles
(D) All three angles