The sides of an isosceles triangle are 5, 5, and 7. How do you find the measure of the vertex angle to the nearest degree?
The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles:
Each with a base of 3.5 and a hypotenuse of 5.
The side opposite the half of the vertex angle is 3.5, the hypotenuse is 5.
The sine function can be used to find the angle.
Use the inverse sin function or a table of trig functions to find the corresponding angle . (Arcsin)
Remember that this is the value of half of the vertex angle so double the value to find the vertex angle.
rounded off to the nearest whole degree =
As all 3 sides of the triangle are known, the cosine rule can be used to find the vertex angle directly.
Using a calculator or tables you can find the angle: