In triangle ABC, the ratio of the angle is A:B:C=2:3:4. What is the measure of the smallest angle?

Question

amistre64 · Answer

the smallest angle is opposite the shortest side

amistre64 · Answer

and we can calculate that angle using a modifies law of cosines

amistre64 · Answer

$$cos^{-1}\left(\frac{short^2 - side^2-other.side^2}{-2(side)(other.side)}\right)=angle$$

amistre64 · Answer

$$cos^{-1}(\frac{2^2 -3^3-4^2}{-2(3)(4)})=angle$$
$$cos^{-1}(\frac{4 -9-16}{-24})=angle$$
$$cos^{-1}(\frac{11}{24})=angle$$

amistre64 · Answer

helps to know how to add... let me fix that

amistre64 · Answer

$$cos^{-1}(\frac{21}{24})=abt.\ .5054^o$$

anonymous · Answer

um thats not any of the choices (1)20 (2)40 (3)60 (4)80

amistre64 · Answer

may calc was on radians :)

amistre64 · Answer

attachment

amistre64 · Answer

$$2^2 = 3^2 + 4^2 -2(3)(4)\  cos(a)$$
$$4 = 9 + 16 -24\  cos(a)$$
$$4-9-16 = -24\  cos(a)$$
$$-21/-24 = cos(a)$$
$$cos^{-1}(21/24) = a$$
or at least it should right?

amistre64 · Answer

that equals about 30 degrees

amistre64 · Answer

but thats aint a choice is it

anonymous · Answer

nope

amistre64 · Answer

the next biggest one = 

9-4-16        11
------- =  ---- ; cos-1(11/16) = abt 47 degrees
-2(2)(4)        16

30 + 47 = 77

180
-77
----
103

amistre64 · Answer

those are the answers; but your choices are either mistyped, or someone messed it up in the program :)

anonymous · Answer

lol its a prep regent

amistre64 · Answer

28.955 degrees is the smallest angle tho ;)  good luck with it

anonymous · Answer

lol thanks for trying