Question

Im not sure how to find the missing angle

Answer 1

Answer:

Step-by-step explanation:

the question is asking for the length of the side labeled x

use Pythagoras'  theorem to find that side

where c = x   because c represents the hypotenuse in the theorem and x is on the hypotenuse in this problem

c = $\sqrt{a^{2} + b^{2} }$

sooo  plug in a = 14 and b = 10

c = $\sqrt{14^{2} + 10^{2} }$

c = $\sqrt{196+100}$

c = $\sqrt{296}$

c= 17.20465.....  ( that's the approx. length of side x in the problem )

since this is a right triangle we could use trigonometry to find the two angles use SOH CAH TOA  to remember how those functions fit on the triangle.

Sin(Ф)=Opp/Hyp  Cos(Ф)=Adj/Hyp  Tan(Ф)=Opp/Adj

since we know the Hyp (hypotenuse) and the side adjacent will be the side with the 10 soooo...

Cos(Ф)=10/17.20465

Ф = arcCos(10/17.20465)

Ф = 54.4623°  is the angle on the side with 10

the side with 14 then has an angle of 35.5376°

:)