Geometry) Two sides in a triangle each have a length of 4 feet. If the angle opposite the base of the triangle is 30°, what are the measures of the three angles of the triangle?

Question

Two sides in a triangle each have a length of 4 feet. If the angle opposite the base of the triangle is 30°, what are the measures of the three angles of the triangle?

A) 30°, 75°, 75°

B) 80°, 70°, 30°

C) 60°, 60°, 65°

D) 90°, 45°, 45°

E) 30°, 30°, 120°

I think the answer is either A or E?

Answer 1

Hi Klauss, this appears to be an isosceles triangle. You can solve this in several ways.

One way:

Drop a perpendicular line from the apex (angle given as 30 degrees) to the base of the triangle. This line splits the triangle into two right triangles.

The sum of the angles of the right triangle equals 180 degrees.

The three angles in one of the right triangles are 15 degrees (one half of the 30 degrees) plus 90 degrees plus x (the missing angle.)

15 + 90 + x = 180

x = 75

The missing angle is 75 degrees.

The correct answer is A, 30 degrees, 75 degrees, and 75 degrees.

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