The isosceles triangle
Answers are for parents and teachers.
1
In an isosceles triangle the vertex angle is 100°. Find each base angle.
(180° − 100°) ÷ 2 = 40°.
2
In an isosceles triangle with AB = AC, B = 4x − 10 and C = 2x + 20. Find x and the vertex angle.
x = 15; base angles 50°; vertex angle 80°.
3
Isosceles Δ ABC has AB = AC = 25 cm and BC = 14 cm. Find the height from A and the area.
Height √(625 − 49) = √576 = 24 cm; area ½ × 14 × 24 = 168 cm².
4
In a 30°–60°–90° triangle the long leg is the short leg times √3. If the short leg is 9 cm, find the hypotenuse and the long leg.
Hypotenuse 18 cm; long leg 9√3 cm (about 15.6 cm).
5
A ramp makes an angle of 30° with the ground and is 6 m long. What height does it reach?
The height is opposite 30°, so it is half of 6 m: 3 m.