Question

given triangle ABC find the values of x and y. In your final answer, include all of your calculations.​

Answer 1

Explanation:

X = ?

y = ?

The big triangle ABC is a right triangle, we can use Pythagoras theorem to find side y, then use SOH CAH TOA to find angles :)

also, there is a special rule for a triangle set up like this one

2CD = BD

for this triangle then,

2CD = 9

CD = 4.5

X = 13.5

now use Pythagoras to find y

`13.5^(2)` =
`6^(2)` +
`y^(2)`

182.25 -36 =
`y^(2)`

`√(146.25)` = y

12.093386 = y

now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find angle B or C, i'll find C

CAH = Cos(C) = Adj / Hyp

Cos(C) = 6 / 13.5

arcCos(Cos(C)) = arcCos(6/13.5)

C = 63.6122°

now find B

180 = 90 + 63.6122 + B

26.3877° = B

got it?