Geometry · Practice

Triangles — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

A triangle has angles of $50°$ and $70°$ . Find the third angle.

Problem 2

A right triangle has legs $6$ and $8$ . Find the hypotenuse.

Problem 3

An equilateral triangle has side length $6$ . Find its perimeter.

Problem 4

An isosceles triangle has an apex angle of $40°$ . Find each base angle.

Problem 5

Find the area of a right triangle with legs $5$ and $12$ .

Problem 6

Find the area of a triangle with sides $3$ , $4$ , and $5$ using Heron's formula.

Problem 7

Two sides of a triangle are $7$ and $10$ , with included angle $60°$ . Find $c^2$ (the square of the opposite side).

Problem 8

Find the circumradius of a triangle with sides $5$ , $12$ , $13$ .

Problem 9

In a triangle, $a = 7$ , $A = 30°$ , $B = 45°$ . Find side $b$ to 2 decimal places.

Problem 10

In triangle $ABC$ , $a = 8$ , $b = 10$ , $A = 30°$ (the angle opposite $a$ ). How many valid triangles exist?

Problem 11

In triangle $ABC$ , the medians divide each side in ratio $1:1$ .

Compute $\dfrac{BD}{DC} \cdot \dfrac{CE}{EA} \cdot \dfrac{AF}{FB}$ to verify Ceva's theorem.