Asked by bryan
In triangle XYZ, XZ=6, ZX=7, and XY=8, find (sinY+sinZ)/sinX.
Answers
Answered by
Reiny
Typo? XZ=6 and ZX=7 ?? , I will assume you meant YZ=7
Use the area of the triangle formula in terms of the sine of the contained angle.
Area = A = (1/2)(7)(8)sinY ---> sinY = A/28
Also A = (1/2)(6)(7)sinZ ----> sinZ = A/21
and A = (1/2)(6)(8)sinX -----> sinX = A/24
(sinY + sinZ)/sinX
= (A/28 + A/21)/(A/24) , divide top and bottom by A
= (1/28 + 1/21)/(1/24)
= (1/12)(24/1)
= 2
Use the area of the triangle formula in terms of the sine of the contained angle.
Area = A = (1/2)(7)(8)sinY ---> sinY = A/28
Also A = (1/2)(6)(7)sinZ ----> sinZ = A/21
and A = (1/2)(6)(8)sinX -----> sinX = A/24
(sinY + sinZ)/sinX
= (A/28 + A/21)/(A/24) , divide top and bottom by A
= (1/28 + 1/21)/(1/24)
= (1/12)(24/1)
= 2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.