The lateral side of an isosceles triangle is 10 cm and forms an angle of 80 degrees

| May 31, 2021 | education

The lateral side of an isosceles triangle is 10 cm and forms an angle of 80 degrees at the apex, find the base and the height drawn to it.

Let a triangle ABC be given, it is isosceles with the base of the AC and the lateral sides AB and BC, AB = BC = 10 cm, as the lateral sides of an isosceles triangle. <B = 80 °, the height drawn to the base of the HV. Find the height of the HV and the base of the speaker.
Consider a triangle ABC, <A = <C – as the angles at the base of an isosceles triangle, then:
180- <B = <A + <C = 2 <A.
180-80 = 2 <A.
<A = <C = 100/2 = 50 °.
Consider a triangle BCH, it is rectangular <H = 90 °, <C = 50 °, by the sine property:
sin C = BH / BC,
BH = sin C * BC = 0.766 * 10 = 7.66 cm.
By the cosine property:
cos C = HC / BC,
HC = cos C * BC = 0.6428 * 10 = 6.42 cm.
Then the base of the triangle is:
AC = 2 * HC = 6.84 cm.
Answer: base 6.84 cm, height 7.66 cm.



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