Question

Find the missing measure indicated in the given triangle.

A) 18 degrees
B) 44 degrees
C) 46 degrees
D) 72 degrees

Answer 1

17.75°

Explanation:

Since it is a right triangle, we can use pythagorean theorem to find the unknown side, side opposite of the angle "?".

Let that side be "x", so we can write (using pythagorean theorem):

`x^2+20^2=21^2\\`

Now, solving for x:

`x^2+20^2=21^2\\x^2+400=441\\x^2=41\\x=√(41)`

Now we use Law of Cosines to solve for the angle "?".

Law of Cosines:
`p^2=a^2+b^2-2abCosP`

Where

p is the side opposite to angle

P is the angle (we want to solve for)

a, and b are the two sides given

Thus, we have:

`p^2=a^2+b^2-2abCosP\\(√(41))^2=21^2+20^2-2(21)(20)CosP\\41=841-840CosP\\840CosP=800\\CosP=0.9524\\P=Cos^(-1)(0.9524)\\P=17.75`