Answer:
135
√
3
y
243
Step-by-step explanation:
It would be <SPA because angle TSV is congruent to angle PSM because they are verticle angles and the vertical angles theorem says that they are congruent angle RPS is congruent to PSM because they are alternating interior angles and angle SMB is congruent to angle SPA because they are alternating interior angles. So, through the process of elimination SPA is not congruent. That is the only angle that can't be congruent by a theorem so the the correct answer is <SPA
Answer:
155.45 cm
Step-by-step explanation:
Given: Length of side x (opposite)= 89.75 cm
Angle is 30°
Lets use tangent rule to find the value of y (adjacent).
∴
Using trigonometry table
⇒
Now, cross multiplying both side
⇒ y=
∴ 155.45 cm is the length of side y.
Solution :
Given :
The height of the person is 5 foot.
The height of the lamppost is 12 foot.
Speed of the person away from the lamppost = 4 ft/s
Let the distance of the tip of the shadow of the perosn to the pole at t seconds after the person started walking away from the pole be d(t).
By similarity of the triangles, we see that
.................(i)
Here x is the distance from the person to the tip of the shadow. As it is given the speed of the person is 4 ft/s, then the distance of the person from the pole 4t. So we have,
x = d - 4t .............(ii)
Putting (ii) in (i) and solving for d is
d(t) = 6.85 t
So now if we derive d(t), we will get the wanted rate of the tip of the shadow.
∴ d'(t) = 6.85 ft/s
5 degrees at 10 pm because it started at 3 then went to 14 which is 17 then went down 12 degrees leaving you with 5 degrees. hope you understand this