Question

The base of an isosceles triangle is 70 centimeters long. The altitude from the vertex angle to the base is 75 centimeters long. Find, to the nearest whole degree, the measure of the base angles of this triangle.

Answer 1

Constructing a triangle for the given data, we get the triangle as shown in the image below. Since the triangle is an isosceles triangle, the two legs AC and BC will be equal in length. Since the length of the sides is equal, the opposite angles will also be equal. So the base angles for the triangle are equal.

We get two similar right angled triangles ADC and BDC. For triangle ADC, AD = 35cm, DC = 75cm. Tangent of angle DAC can be written as:

$tan(DAC)= \frac{CD}{DA} \\ \\ tan(DAC)= \frac{75}{35}= \frac{15}{7}$

Angle DAC is equal to tangent inverse of 15/7 which equals 65 degrees, rounded of to nearest whole degree.

Angle DBC = DAC = 65 degrees

Thus the base angles for the given isosceles triangle will be 65 degrees each, rounded of to nearest whole degree.