Answer:
1st pic) 17.8
2nd pic) 16.8
3rd pic) 9.1
4th pic) 13.5
Step-by-step explanation:
<u>1st pic:</u>
(write equation) Cos 27 (cos 27 = 0.89) = 
(new equation) 0. 89 = 
(multiply 20 on both sides) 0.89 x 20 =
x 20
(solve) 17.8 = x
<u>2nd pic:</u> 
(write equation) tan 40 (tan 40 = 0.84) = 
(new equation) 0.84 = 
(multiply 32 on both sides) 0.84 x 20 =
x 20
(solve) 16.8 = x
<u>3rd pic:</u> 
(write equation) cos 55 (cos 55 = 0.57) = 
(new equation) 0.57 = 
(multiply 16 on both sides) 0.57 x 16 =
x 16
(solve) 9.1 = x
<u>4th pic:</u> 
(write eqaution) tan 42 (tan 42 = 0.90) = 
(new equation) 0.90 = 
(multiply 15 on both sides) 0.90 x 15 =
x 15
(solve) 13.5 = x
I'd say that, if the angles S and U are equal, as the SV and UV segments move towards each other, they meet at vertex V, the angles they make, angle SVT and UVT, have to be equal, because the side TV is shared by both, and has the same direction.
now, side TV is on both triangles, and is shared by both, so is the same length, so TV on one triangle is equal to TV on the other
check the picture below
so, you have one Angle, another Angle, and then a Side
A A S