Question

PLEASE HELP!!!

find the missing information for the triangle. make sure to find the missing angle measure AND the 2 missing side lengths

Answer 1

Below

Explanation:

REMEMBER: for a right triangle sin (30) = opposite LEG/ hypotenuse

so sin 30 = 4 / hypotenuse now, with a calculator sin 30 = 1/2

1/2 = 4 / hypotenuse so hypotenuse = 8

Now it is a right triangle so Pythagorean theorem applies

hyp ^2 = 4 ^2 + BM^2

8^2 = 4^2 + BM^2

48 = BM^2 so BM = sqrt (48 ) = 4 sqrt 3

Finally, all of the internal angles of ANY triangle sum to 180 °

so angle x = 180 - 90 - 30 = 60°

Answer 2

Sides:

MX = 4cm

BX = 8cm

BM = 6.928...cm

Angles:

m = 90°

b = 30°

x = 60°

Explanation:

We've been given 3 pieces of info that we can use, which is more than enough

Using the sine rule, we can find the hypotenuse:

`(4cm)/(sin30) = (BXcm)/(sin90)`→
`(4sin90)/(sin30) =BX = 8cm`

Now we can use Pythagoras' theorem to find the last side:

`a^2+b^2=c^2` →
`b^2\ = c^2-a^2` →
`64 - 16 = b^2 = 48` →
`√(48) =6.928...cm`

And since we know two of the angles, we can find the third:

`x = 180 - (30 + 90) = 180 - 120 = 60`°