Geometry and Trigonometry Practice Questions
SAT · SAT Math · 144 free MCQs with instant results and detailed explanations.
144
Total
38
Easy
86
Medium
20
Hard
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Sample Questions from Geometry and Trigonometry
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the area of a triangle with a base of 10 units and a height of 5 units?
A.
25 square units
B.
30 square units
C.
50 square units
D.
15 square units
Show Answer & Explanation
Correct Answer: A
The area of a triangle is calculated using the formula: Area = 1/2 * base * height. Substituting the values, Area = 1/2 * 10 * 5 = 25 square units.
Q2
Easy
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 units long, what is the length of the side opposite to the 30-degree angle?
A.
5 units
B.
10 units
C.
โ10 units
D.
โ3 units
Show Answer & Explanation
Correct Answer: A
In a 30-60-90 triangle, the side opposite the 30-degree angle is half the hypotenuse. Thus, the length of the opposite side is 10/2 = 5 units.
Q3
Easy
A circle has a radius of 4 units. What is the circumference of the circle?
A.
8ฯ units
B.
12ฯ units
C.
16ฯ units
D.
20ฯ units
Show Answer & Explanation
Correct Answer: A
The circumference of a circle is calculated using the formula: Circumference = 2ฯr, where r is the radius. Thus, Circumference = 2ฯ * 4 = 8ฯ units.
Q4
Medium
In triangle ABC, angle A measures 45 degrees and angle B measures 60 degrees. What is the measure of angle C?
A.
75 degrees
B.
90 degrees
C.
105 degrees
D.
120 degrees
Show Answer & Explanation
Correct Answer: A
The angles in a triangle sum up to 180 degrees. Therefore, angle C = 180 - (45 + 60) = 75 degrees.
Q5
Medium
A rectangular garden has a length of 20 meters and a width of 15 meters. What is the diagonal length of the garden?
A.
25 meters
B.
30 meters
C.
35 meters
D.
20โ2 meters
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean theorem, the diagonal d = โ(lengthยฒ + widthยฒ) = โ(20ยฒ + 15ยฒ) = โ(400 + 225) = โ625 = 25 meters.
Q6
Medium
What is the exact value of sin(30 degrees)?
A.
1/2
B.
โ3/2
C.
1
D.
โ2/2
Show Answer & Explanation
Correct Answer: A
From trigonometric values, sin(30 degrees) is known to equal 1/2, which is a standard angle in trigonometry.
Q7
Medium
A circular fountain has a radius of 10 feet. What is the area of the fountain?
A.
100ฯ square feet
B.
50ฯ square feet
C.
25ฯ square feet
D.
200ฯ square feet
Show Answer & Explanation
Correct Answer: A
The area of a circle is calculated using the formula A = ฯrยฒ. Thus, A = ฯ(10)ยฒ = 100ฯ square feet.
Q8
Hard
In a right triangle, one angle measures 30 degrees. If the hypotenuse is 10 units, what is the length of the side opposite the 30-degree angle?
A.
5
B.
10
C.
7.5
D.
8.66
Show Answer & Explanation
Correct Answer: A
In a right triangle with a 30-degree angle, the side opposite the 30-degree angle is always half the length of the hypotenuse. Therefore, the length of the side opposite the 30-degree angle is 10 units (hypotenuse) divided by 2, which equals 5 units.
Q9
Hard
In a triangle ABC, if angle A measures 45 degrees, angle B measures 60 degrees, and the length of side a (opposite angle A) is 10 cm, what is the length of side b (opposite angle B)?
A.
8.66 cm
B.
7.5 cm
C.
9.15 cm
D.
11.32 cm
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines, we have a / sin(A) = b / sin(B). Plugging in the values: 10 / sin(45) = b / sin(60). Calculating gives b = 10 * (sin(60) / sin(45)) = 10 * (โ3/2 / โ2/2) = 10 * โ3 = 8.66 cm.
Q10
Hard
A circle is inscribed in a triangle with sides 10 cm, 24 cm, and 26 cm. What is the radius of the inscribed circle?
A.
5 cm
B.
6 cm
C.
8 cm
D.
7 cm
Show Answer & Explanation
Correct Answer: B
The radius r of the inscribed circle is given by the formula r = A/s, where A is the area of the triangle and s is the semiperimeter. The triangle is a right triangle, area A = 0.5 * base * height = 0.5 * 10 * 24 = 120. The semiperimeter s = (10 + 24 + 26) / 2 = 30. Therefore, r = 120 / 30 = 6 cm.
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Geometry and Trigonometry โ SAT SAT Math Practice Questions Online
This page contains 144 practice MCQs for the chapter Geometry and Trigonometry in SAT SAT Math. The questions are organized by difficulty โ 38 easy, 86 medium, 20 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.