Question

In an acute angle triangle ABC if tan angle A + Angle B minus angle C is equals to root 3 and sec angle B + angle C minus angle A is equals to 1 find Angle A Angle B and angle C

Answer 1

Answer:

Step-by-step explanation:

tan(A+B-C)=√3              tan60=√3

sec(B+C-A)=1                 sec0=1

therefore,

B+C-A=0

B+C=A ------------(1)

Also,

A+B-C=60

B+C+B-C=60  (from 1)

2B=60

B=30 -----------(2)

Also,

A-C=B  (FROM 1)

A-C=30°---------(3)

A+B+C=180°     (Angle sum property)

A+C=180° - B

A+C=180°-30°  (from 2)

A+C=150° --------(4)

Now, Adding 3 and 4,

2A=150°+30°

A=180°/2=90°

therefore C=150°-90°=60°

Finally, angle A =90°,angle B=30° and angle C=60°

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