Geometry and Trigonometry MCQ Quiz - Objective Question with Answer for Geometry and Trigonometry - Download Free PDF

Geometry and Trigonometry Question 1:

In triangle $XYZ$, angle $X$ is $45\text{degree}$, and triangle $XYZ$ is similar to triangle $PQR$. What is the measure of angle $P$?

Geometry and Trigonometry Question 2:

A triangle has sides of length 5, 12, and a hypotenuse. What is the length of the hypotenuse?

Geometry and Trigonometry Question 3:

In an isosceles right triangle, the hypotenuse measures $10\sqrt{2}$ centimeters. What is the length of each leg of the triangle?

Geometry and Trigonometry Question 4:

Two similar triangles $\mathrm{△}KLM$ and $\mathrm{△}NOP$ have $\mathrm{\angle }K=\mathrm{\angle }N$ and $\mathrm{\angle }M=\mathrm{\angle }P$ as right angles. If $\tan L=\sqrt{3}$ and $NP=80$, what is the length of $NO$?

Geometry and Trigonometry Question 5:

A circular track is designed for a jogging path. If a jogger runs along an arc measuring $\frac{5\pi }{12}$ radians, what is the measure of this arc in degrees?

A triangular prism has a height of 8 centimeters (cm) and a volume of 216 cm³. What is the area, in cm², of the base of the prism? (The volume of a triangular prism is equal to Bh, where B is the area of the base and h is the height of the prism.)

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

A. 11

B. 22

C. 44

D. 66

A circle has a circumference of 31π centimeters. What is the diameter, in centimeters, of the circle?

A right circular cone has a height of 22 centimeters (cm) and a base with a diameter of 6 cm. The volume of this cone is nπ cm³. What is the value of n ? 

A triangle with angle measures 30°, 60°, and 90° has a perimeter of $18+6\sqrt{3}$. What is the length of the longest side of the triangle?

In the figure above, $\overline{BD}$ is parallel to $\overline{AE}$.

What is the length of $\overline{CE}$ ?

Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angle C corresponds to angle F. Angles C and F are right angles. If $\tan (A)=\frac{50}{7}$, what is the value of tan(E) ?

In a right triangle, the tangent of one of the two acute angles is $\frac{\sqrt{3}}{3}$. What is the tangent of the other acute angle?

A. $-\frac{\sqrt{3}}{3}$

B. $-\frac{3}{\sqrt{3}}$

C. $\frac{\sqrt{3}}{3}$

D. $\frac{3}{\sqrt{3}}$

Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angles C and F are right angles. The length of $\overline{AB}$ is 2.9 times the length of $\overline{DE}$. If $\tan A=\frac{21}{20}$, what is the value of sin D ?

The length of a rectangle's diagonal is $3\sqrt{17}$, and the length of the rectangle's shorter side is 3. What is the length of the rectangle's longer side?