two angles of a triangle are the measures 60 and 75 find the measurement of the third angle
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two angles of a triangle are the measures 60 and 75 find the measurement of the third angle
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In triangle ABC , angle A= 60° , angle B = 75° , angle C= 180°- (60°+75°) = 45° .
By the sine rule :- a/sin A = b/sinB = c/sinC
a/Sin 60°/a = b/sin75° = c/sin45° = k(let).
a = k.sin60° = k.(√3/2).
b = k.sin75° = k.sin(45°+30°) = k.(sin45°.cos30°+cos45°sin30°)=k.(√3+1)/2√2.
c = k.sin45° = k.(1/√2).
Thus, a. : b : c = k.(√3/2) : k.(√3+1)/2√2 : k.(1/√2). , multiplying by 2√2/k.
or, a : b : c. = (√6) : (√3+1) : (2)
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Answer:
first of all thanks for asking this question!! and here is your answer mate ♥️
Step-by-step explanation:
let us take the angles as a,b,c
atq
a=60
b=75
a+b+c=180(angle sum property)
60+75+c=180
135+c=180
c=180-135
c=45