If the angle of a triangle are 30°,75°,and 75°. then the sides are in the ratio
Answers
Answer:
Since the ratio of 30:75 reduces to 2:5, this verifies the answer. Note: it is IMPOSSIBLE to have both an isosceles triangle AND have a base angle that is greater than 90 degrees.
Step-by-step explanation:
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Answer:
In triangle ABC Angle A=30° , B=75° and C=75°. Here angle B= angle C.
Therefore length of side b= length of side c. = x units (let).
we know that:-
a = b.cosC+c.cosB , putting b=c=x. and B=C =75°
a= x.cos75°+x.cos75° =2.x.cos75°. = 2.x.cos(45+30)
a=2.x.(cos45.cos30-sin45.sin30)
a = 2.x.1/√2.(√3–1)/2. =(√3–1).x/√2.
a : b : c = (√3–1).x/√2 : x : x. = (√3–1) : √2 : √2 .
a : b : c = (√3–1)/(√3–1). : √2/(√3–1) : √2/(√3–1)
a : b : c. = 1. : √2.(√3+1)/(√3–1)(√3+1). : √2.(√3+1)/(√3–1)(√3+1).
a : b : c = 1 : √2.(√3+1)/2. : √2.(√3+1)/2.
a : b : c = 1. : (√3+1)/√2. : (√3+1)/√2.